{VERSION 5 0 "Windows XP" "5.0" }
{USTYLETAB {PSTYLE "Normal256" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12
 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "H
eading 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 1 1 2 2 2 2 1 
0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 5" -1 201 1
 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 
3 2 144 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1" -1 202 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 
-1 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0
 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Bul
let Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 
0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified Maple Out
put" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1
 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 
-1 "Courier" 1 9 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 
2 -1 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1
 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnosti
c" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 10 64 128 64 1 2 2 2 2 2 1 1 0 
0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE 
"" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0
 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 203 1 {CSTYLE "" -1 -1 "Times" 
1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2 0 2 2 -1 1 }
{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2
 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal" -1 0 
1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0
 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Annotation Title" -1 204 1 {CSTYLE "" -1
 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 
2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 
0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Headin
g 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 0 0 1 
}1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 4" -1 205 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3
 2 108 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "
Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 
}{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2
 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed \+
Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1
 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0
 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courie
r" 1 10 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2
 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 1" -1
 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 
0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Time
s" 1 18 0 0 0 1 2 1 1 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }
{PSTYLE "Ordered List 2" -1 206 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 
1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 }{CSTYLE "2D Math
 Italic Small204" -1 200 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }
{CSTYLE "Help Variable" -1 25 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0
 1 }{CSTYLE "Text" -1 201 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }
{CSTYLE "Help Bold" -1 39 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "Page Number" -1 33 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }
{CSTYLE "2D Math Italic Small" -1 202 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 
0 0 0 1 }{CSTYLE "Help Nonterminal" -1 24 "Courier" 1 12 0 0 0 1 2 1 2
 2 2 2 0 0 0 1 }{CSTYLE "Default" -1 38 "Times" 1 12 0 0 0 1 2 2 2 2 2
 2 0 0 0 1 }{CSTYLE "Maple Comment" -1 21 "Courier" 1 12 0 0 0 1 2 1 2
 2 2 2 0 0 0 1 }{CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 
1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math Small" -1 7 "Times" 1 1 0 0 0 1 2 
2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Inert Output" -1 203 "Times" 1 12 144 
144 144 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Help Fixed" -1 23 "Courier" 1 
10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small207" -1 
204 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Popup" -1 31 "Ti
mes" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Plot Title" -1 27 
"Times" 1 10 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Ti
mes" 1 12 255 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Copyright" -1 34 "Ti
mes" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input Placeholde
r" -1 205 "Courier" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D \+
Math Bold Small" -1 10 "Times" 1 1 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }
{CSTYLE "2D Math Italic Small202" -1 206 "Times" 1 1 0 0 0 1 1 2 2 2 2
 2 0 0 0 1 }{CSTYLE "Annotation Text" -1 207 "Times" 1 12 0 0 0 1 2 2 
2 2 2 2 0 0 0 1 }{CSTYLE "Help Notes" -1 37 "Times" 1 12 0 0 0 1 2 1 2
 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Bold" -1 41 "Times" 1 12 0 0 
0 1 1 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small205" -1 208 "Tim
es" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "Times"
 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Symbol 2" -1 
16 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Equation Label" 
-1 209 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Ital
ic Small206" -1 210 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "
Plot Text" -1 28 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hel
p Italic" -1 42 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hel
p Heading" -1 26 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Ou
tput Labels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "H
elp Normal" -1 30 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2
D Comment" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "He
lp Maple Name" -1 35 "Times" 1 12 104 64 92 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 2 0 0 0 1 }
{CSTYLE "Dictionary Hyperlink" -1 45 "Times" 1 12 147 0 15 1 2 2 1 2 2
 2 0 0 0 1 }{CSTYLE "Help Emphasized" -1 22 "Times" 1 12 0 0 0 1 1 2 2
 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 40 "Times" 1 12 0 0 0 1 
1 2 2 2 2 2 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Times" 1 12 0 0 0 1 2 2 2 
2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "Times" 1 12 0 0 0 1 2 1 2 2
 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2
 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times" 1 12 0 0 0 1 2 2 1 2
 2 2 0 0 0 1 }{CSTYLE "Help Underlined Italic" -1 43 "Times" 1 12 0 0 
0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold" -1 5 "Times" 1 12 0 0 
0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic" -1 3 "Times" 1 12 0 
0 0 1 1 2 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 207 1 {CSTYLE "" -1 -1 "Times
" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{CSTYLE "" -1 211 "Times" 1 16 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{PSTYLE ""
 -1 208 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1
 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{CSTYLE "" -1 212 "Helvetica" 1 14 0 0 0 
1 2 1 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 209 1 {CSTYLE "" -1 -1 "Times" 1 
12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{CSTYLE 
"" -1 213 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 214 
"Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 215 "Times" 1 
12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 210 1 {CSTYLE "" -1 -1 "
Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 
}{CSTYLE "" -1 216 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "
" -1 217 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 218 "
Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 211 1 {CSTYLE "
" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 
2 2 -1 1 }{CSTYLE "" -1 219 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "" -1 220 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 221 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 222 "T
imes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 223 "Times" 1 12
 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 212 1 {CSTYLE "" -1 -1 "Ti
mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }
{CSTYLE "" -1 224 "Times" 1 14 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 225 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 226 "T
imes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }}
{SECT 0 {EXCHG {PARA 207 "" 0 "" {TEXT 211 41 "Lab2 - Integration, Nu
merical integration" }}}{SECT 1 {PARA 208 "" 0 "" {TEXT 201 11 "Integr
ation" }{TEXT 212 0 "" }}{SECT 1 {PARA 209 "" 0 "" {TEXT 201 30 "Basic
s of integration in Maple" }}{PARA 0 "" 0 "" {TEXT 227 0 "" }{TEXT 
201 89 "To write the symbol for an integral, either definite or indefi
nite, use capitalized  Int:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "Int(sin(x),x);" }{TEXT 227 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "Int(sin(x),x=1..2);" }}}{PARA 0 "" 0 "" {TEXT 227 46 
"To calculate the integral, use either command " }{TEXT 213 5 "value" 
}{TEXT 227 11 " or lowcase" }{TEXT 214 5 " int:" }{TEXT 227 1 " " }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 14 "int(sin(x),x);" }}}{EXCHG {PARA 0 "> " 0 ""
 {MPLTEXT 1 0 23 "int(sin(x),x=0..Pi/2); " }{TEXT 227 0 "" }{TEXT 201 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 0 1 "Typesetting:-mrow(Types
etting:-mi(\"int\", italic = \"false\", mathvariant = \"bold\", fontwe
ight = \"bold\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-
mi(\"sec\", italic = \"false\", mathvariant = \"bold\", fontweight = \+
\"bold\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x
\", italic = \"false\", mathvariant = \"bold\", fontweight = \"bold\")
), mathvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"&
sdot;\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"fals
e\", separator = \"false\", stretchy = \"false\", symmetric = \"false
\", largeop = \"false\", movablelimits = \"false\", accent = \"false\"
, lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"tan\", it
alic = \"false\", mathvariant = \"bold\", fontweight = \"bold\"), Type
setting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", italic = \"t
rue\", mathvariant = \"bold-italic\", fontweight = \"bold\")), mathvar
iant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\",\", mathva
riant = \"bold\", fontweight = \"bold\", fence = \"false\", separator \+
= \"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"f
alse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0e
m\", rspace = \"0.3333333em\"), Typesetting:-mi(\"x\", italic = \"true
\", mathvariant = \"bold-italic\", fontweight = \"bold\")), mathvarian
t = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\";\", mathvaria
nt = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \+
\"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"fal
se\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em
\", rspace = \"0.2777778em\"));" "-I%mrowG6#/I+modulenameG6\"I,Typeset
tingGI(_syslibGF'6%-I#miGF$6&Q$intF'/%'italicGQ&falseF'/%,mathvariantG
Q%boldF'/%+fontweightGF4-I(mfencedGF$6%-F#6)-F,6&Q$secF'F/F2F5-F86%-F#
6#-F,6&Q\"xF'F/F2F5F2F5-I#moGF$6.Q'⋅F'F2F5/%&fenceGF1/%*separator
GF1/%)stretchyGF1/%*symmetricGF1/%(largeopGF1/%.movablelimitsGF1/%'acc
entGF1/%'lspaceGQ&0.0emF'/%'rspaceGFZ-F,6&Q$tanF'F/F2F5-F86%-F#6#-F,6&
FE/F0Q%trueF'/F3Q,bold-italicF'F5F2F5-FG6.Q\",F'F2F5FJ/FMFaoFNFPFRFTFV
FX/FfnQ,0.3333333emF'F^oF2F5-FG6.Q\";F'F2F5FJFgoFNFPFRFTFVFX/FfnQ,0.27
77778emF'" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mro
w(Typesetting:-mi(\"Int\", bold = \"true\", italic = \"false\", mathva
riant = \"bold\", fontweight = \"bold\"), Typesetting:-mfenced(Typeset
ting:-mrow(Typesetting:-msup(Typesetting:-mi(\"x\", bold = \"true\", i
talic = \"false\", mathvariant = \"bold\", fontweight = \"bold\"), Typ
esetting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \+
\"bold\", fontweight = \"bold\")), superscriptshift = \"0\"), Typesett
ing:-mo(\"+\", bold = \"true\", mathvariant = \"bold\", fontweight = \+
\"bold\", fence = \"false\", separator = \"false\", stretchy = \"false
\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals
e\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.222222
2em\"), Typesetting:-mn(\"3\", bold = \"true\", mathvariant = \"bold\"
, fontweight = \"bold\"), Typesetting:-mo(\"⋅\", bold = \"true\",
 mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", sep
arator = \"false\", stretchy = \"false\", symmetric = \"false\", large
op = \"false\", movablelimits = \"false\", accent = \"false\", lspace \+
= \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"x\", bold = \"true
\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"b
old\"), Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \"
bold\", fontweight = \"bold\", fence = \"false\", separator = \"false
\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+
movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em
\", rspace = \"0.2222222em\"), Typesetting:-mn(\"7\", bold = \"true\",
 mathvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\",\"
, bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fenc
e = \"false\", separator = \"true\", stretchy = \"false\", symmetric =
 \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+
\"false\", lspace = \"0.0em\", rspace = \"0.3333333em\"), Typesetting:
-mi(\"x\", bold = \"true\", italic = \"true\", mathvariant = \"bold-it
alic\", fontweight = \"bold\"), Typesetting:-mo(\"=\", bold = \"true\"
, mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", se
parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg
eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace
 = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mn(\"0\", \+
bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\"), Types
etting:-mo(\"..\", bold = \"true\", mathvariant = \"bold\", fontweight
 = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"fa
lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f
alse\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.0em
\"), Typesetting:-mn(\"4\", bold = \"true\", mathvariant = \"bold\", f
ontweight = \"bold\")), bold = \"true\", mathvariant = \"bold\", fontw
eight = \"bold\"), Typesetting:-mo(\";\", bold = \"true\", mathvariant
 = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \"t
rue\", stretchy = \"false\", symmetric = \"false\", largeop = \"false
\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\",
 rspace = \"0.2777778em\"), Typesetting:-mi(\"value\", bold = \"true\"
, italic = \"false\", mathvariant = \"bold\", fontweight = \"bold\"), \+
Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"%\", bold = \+
\"true\", italic = \"false\", mathvariant = \"bold\", fontweight = \"b
old\")), mathvariant = \"normal\"), Typesetting:-mo(\";\", bold = \"tr
ue\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\"
, separator = \"true\", stretchy = \"false\", symmetric = \"false\", l
argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp
ace = \"0.0em\", rspace = \"0.2777778em\"));" "-I%mrowG6#/I+modulename
G6\"I,TypesettingGI(_syslibGF'6(-I#miGF$6'Q$IntF'/%%boldGQ%trueF'/%'it
alicGQ&falseF'/%,mathvariantGQ%boldF'/%+fontweightGF7-I(mfencedGF$6&-F
#6/-I%msupGF$6%-F,6'Q\"xF'F/F2F5F8-F#6#-I#mnGF$6&Q\"2F'F/F5F8/%1supers
criptshiftGQ\"0F'-I#moGF$6/Q\"+F'F/F5F8/%&fenceGF4/%*separatorGF4/%)st
retchyGF4/%*symmetricGF4/%(largeopGF4/%.movablelimitsGF4/%'accentGF4/%
'lspaceGQ,0.2222222emF'/%'rspaceGF\\o-FH6&Q\"3F'F/F5F8-FO6/Q'⋅F'F
/F5F8FRFTFVFXFZFfnFhn/F[oQ&0.0emF'/F^oFfo-F,6'FDF//F3F1/F6Q,bold-itali
cF'F8-FO6/Q(−F'F/F5F8FRFTFVFXFZFfnFhnFjnF]o-FH6&Q\"7F'F/F5F8-FO6
/Q\",F'F/F5F8FR/FUF1FVFXFZFfnFhnFeo/F^oQ,0.3333333emF'Fho-FO6/Q\"=F'F/
F5F8FRFTFVFXFZFfnFhn/F[oQ,0.2777778emF'/F^oF]q-FH6&Q\"0F'F/F5F8-FO6/Q#
..F'F/F5F8FRFTFVFXFZFfnFhnFjnFgo-FH6&Q\"4F'F/F5F8F/F5F8-FO6/Q\";F'F/F5
F8FRFfpFVFXFZFfnFhnFeoF^q-F,6'Q&valueF'F/F2F5F8-F;6$-F#6#-F,6'Q\"%F'F/
F2F5F8/F6Q'normalF'Fhq" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 0 1 "Type
setting:-mrow(Typesetting:-mi(\"int\", italic = \"false\", mathvariant
 = \"bold\", fontweight = \"bold\"), Typesetting:-mfenced(Typesetting:
-mrow(Typesetting:-msup(Typesetting:-mi(\"x\", italic = \"false\", mat
hvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mrow(Typeset
ting:-mn(\"2\", mathvariant = \"bold\", fontweight = \"bold\")), super
scriptshift = \"0\"), Typesetting:-mo(\"+\", mathvariant = \"bold\", f
ontweight = \"bold\", fence = \"false\", separator = \"false\", stretc
hy = \"false\", symmetric = \"false\", largeop = \"false\", movablelim
its = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace \+
= \"0.2222222em\"), Typesetting:-mn(\"3\", mathvariant = \"bold\", fon
tweight = \"bold\"), Typesetting:-mo(\"⋅\", mathvariant = \"bold
\", fontweight = \"bold\", fence = \"false\", separator = \"false\", s
tretchy = \"false\", symmetric = \"false\", largeop = \"false\", movab
lelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace =
 \"0.0em\"), Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \+
\"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"−\", \+
mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", sepa
rator = \"false\", stretchy = \"false\", symmetric = \"false\", largeo
p = \"false\", movablelimits = \"false\", accent = \"false\", lspace =
 \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn(\"7\", ma
thvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\",\", m
athvariant = \"bold\", fontweight = \"bold\", fence = \"false\", separ
ator = \"true\", stretchy = \"false\", symmetric = \"false\", largeop \+
= \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+
\"0.0em\", rspace = \"0.3333333em\"), Typesetting:-mo(\" \", mathvaria
nt = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \+
\"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa
lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em
\", rspace = \"0.0em\"), Typesetting:-mi(\"x\", italic = \"true\", mat
hvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"
=\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\",
 separator = \"false\", stretchy = \"false\", symmetric = \"false\", l
argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp
ace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mn(\"0
\", mathvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"
..\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\"
, separator = \"false\", stretchy = \"false\", symmetric = \"false\", \+
largeop = \"false\", movablelimits = \"false\", accent = \"false\", ls
pace = \"0.2222222em\", rspace = \"0.0em\"), Typesetting:-mn(\"4\", ma
thvariant = \"bold\", fontweight = \"bold\")), mathvariant = \"bold\",
 fontweight = \"bold\"), Typesetting:-mo(\";\", bold = \"false\", math
variant = \"normal\", fence = \"false\", separator = \"true\", stretch
y = \"false\", symmetric = \"false\", largeop = \"false\", movablelimi
ts = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.2
777778em\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6
%-I#miGF$6&Q$intF'/%'italicGQ&falseF'/%,mathvariantGQ%boldF'/%+fontwei
ghtGF4-I(mfencedGF$6%-F#60-I%msupGF$6%-F,6&Q\"xF'F/F2F5-F#6#-I#mnGF$6%
Q\"2F'F2F5/%1superscriptshiftGQ\"0F'-I#moGF$6.Q\"+F'F2F5/%&fenceGF1/%*
separatorGF1/%)stretchyGF1/%*symmetricGF1/%(largeopGF1/%.movablelimits
GF1/%'accentGF1/%'lspaceGQ,0.2222222emF'/%'rspaceGFin-FE6%Q\"3F'F2F5-F
L6.Q'⋅F'F2F5FOFQFSFUFWFYFen/FhnQ&0.0emF'/F[oFco-F,6&FA/F0Q%trueF'
/F3Q,bold-italicF'F5-FL6.Q(−F'F2F5FOFQFSFUFWFYFenFgnFjn-FE6%Q\"7
F'F2F5-FL6.Q\",F'F2F5FO/FRFhoFSFUFWFYFenFbo/F[oQ,0.3333333emF'-FL6.Q\"
~F'F2F5FOFQFSFUFWFYFenFboFdoFeo-FL6.Q\"=F'F2F5FOFQFSFUFWFYFen/FhnQ,0.2
777778emF'/F[oF^q-FE6%Q\"0F'F2F5-FL6.Q#..F'F2F5FOFQFSFUFWFYFenFgnFdo-F
E6%Q\"4F'F2F5F2F5-FL6.Q\";F'/%%boldGF1/F3Q'normalF'FOFdpFSFUFWFYFenFbo
F_q" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 201 84 "Remember the difference b
etween pi (just a greek letter) and Pi (the number 3.14...)" }{TEXT 
227 0 "" }}}{PARA 0 "" 0 "" {TEXT 227 0 "" }}{PARA 0 "" 0 "" {TEXT 
227 21 "It's  helpful to use " }{TEXT 215 4 "Int " }{TEXT 227 114 "- b
y comparing the output of Int with the given integral, you make sure t
hat you haven't made any typing mistakes." }}}{PARA 0 "" 0 "" {TEXT 
227 0 "" }}}{SECT 1 {PARA 210 "" 0 "" {TEXT 201 30 "Numerical integrat
ion in Maple" }}{PARA 3 "" 0 "" {TEXT 228 0 "" }{TEXT 216 0 "" }{TEXT 
201 85 "There are commands to apply approximate integration methods th
at we studied in class." }}{PARA 0 "" 0 "" {TEXT 227 34 "They are cont
ained in the package " }{TEXT 217 8 "student." }}{EXCHG {PARA 0 "> " 0
 "" {MPLTEXT 1 0 23 "restart; with(student);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT 227 55 "We are going to calculate approximately the value of a
 " }{TEXT 218 8 "definite" }{TEXT 227 10 " integral:" }}{PARA 0 "" 0 "
" {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"tr
ue\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-msubsu
p(Typesetting:-mo(\"∫\", foreground = \"[144,144,144]\", mathvaria
nt = \"normal\", Typesetting:-msemantics = \"inert\", fence = \"false
\", separator = \"false\", stretchy = \"false\", symmetric = \"false\"
, largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+
lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"a\", italic
 = \"true\", mathvariant = \"italic\"), Typesetting:-mi(\"b\", italic \+
= \"true\", mathvariant = \"italic\"), superscriptshift = \"2\", subsc
riptshift = \"0\"), Typesetting:-mi(\"\", italic = \"true\", mathvaria
nt = \"italic\"), Typesetting:-mrow(Typesetting:-mi(\"f\", italic = \"
true\", mathvariant = \"italic\"), Typesetting:-mo(\"⁡\"
, mathvariant = \"normal\", fence = \"false\", separator = \"false\", \+
stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mova
blelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace \+
= \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(
\"x\", italic = \"true\", mathvariant = \"italic\")), mathvariant = \"
normal\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"i
talic\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.3em\", d
epth = \"0.0ex\", linebreak = \"auto\"), Typesetting:-mo(\"&Differenti
alD;\", foreground = \"[144,144,144]\", mathvariant = \"normal\", Type
setting:-msemantics = \"inert\", fence = \"false\", separator = \"fals
e\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\",
 movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rs
pace = \"0.0em\"), Typesetting:-mi(\"x\", italic = \"true\", mathvaria
nt = \"italic\")), Typesetting:-mi(\"\", italic = \"true\", mathvarian
t = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslib
GF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6)-I(
msubsupGF$6'-I#moGF$6/Q&∫F'/%+foregroundGQ.[144,144,144]F'/F3Q'nor
malF'/I+msemanticsGF$Q&inertF'/%&fenceGQ&falseF'/%*separatorGFH/%)stre
tchyGFH/%*symmetricGFH/%(largeopGFH/%.movablelimitsGFH/%'accentGFH/%'l
spaceGQ&0.0emF'/%'rspaceGFW-F,6%Q\"aF'F/F2-F,6%Q\"bF'F/F2/%1superscrip
tshiftGQ\"2F'/%/subscriptshiftGQ\"0F'F+-F#6%-F,6%Q\"fF'F/F2-F;6-Q0&App
lyFunction;F'FAFFFIFKFMFOFQFSFUFX-I(mfencedGF$6$-F#6#-F,6%Q\"xF'F/F2FA
F+-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.3emF'/%&depthGFep/%*li
nebreakGQ%autoF'-F;6/Q0ⅆF'F>FAFCFFFIFKFMFOFQFSFUFXF]pF+"
 }}}{SECT 1 {PARA 211 "" 0 "" {TEXT 201 15 "Midpoint Method" }}{PARA 0
 "" 0 "" {TEXT 227 29 "For this method, use command " }{TEXT 219 11 "m
iddlesum. " }{TEXT 227 147 "First argument is the integrand, second is
 the variable and interval of integration, third is the number of  pie
ces (strips), usually denoted by n." }}{PARA 0 "" 0 "" {TEXT 227 18 "C
onsider integral " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(
\"\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(
Typesetting:-msubsup(Typesetting:-mo(\"∫\", foreground = \"[144,14
4,144]\", mathvariant = \"normal\", Typesetting:-msemantics = \"inert
\", fence = \"false\", separator = \"false\", stretchy = \"false\", sy
mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesettin
g:-mn(\"1\", mathvariant = \"normal\"), Typesetting:-mn(\"2\", mathvar
iant = \"normal\"), superscriptshift = \"2\", subscriptshift = \"0\"),
 Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), T
ypesetting:-mrow(Typesetting:-mi(\"sin\", italic = \"false\", mathvari
ant = \"normal\"), Typesetting:-mo(\"⁡\", mathvariant = \+
\"normal\", fence = \"false\", separator = \"false\", stretchy = \"fal
se\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fa
lse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Ty
pesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"
true\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-msup
(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), \+
Typesetting:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \+
\"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"ital
ic\")), mathvariant = \"normal\")), Typesetting:-mi(\"\", italic = \"t
rue\", mathvariant = \"italic\"), Typesetting:-mspace(height = \"0.0ex
\", width = \"0.3em\", depth = \"0.0ex\", linebreak = \"auto\"), Types
etting:-mo(\"ⅆ\", foreground = \"[144,144,144]\", mathva
riant = \"normal\", Typesetting:-msemantics = \"inert\", fence = \"fal
se\", separator = \"false\", stretchy = \"false\", symmetric = \"false
\", largeop = \"false\", movablelimits = \"false\", accent = \"false\"
, lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"x\", ital
ic = \"true\", mathvariant = \"italic\")), Typesetting:-mi(\"\", itali
c = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6
\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,mathv
ariantGQ'italicF'-F#6)-I(msubsupGF$6'-I#moGF$6/Q&∫F'/%+foregroundG
Q.[144,144,144]F'/F3Q'normalF'/I+msemanticsGF$Q&inertF'/%&fenceGQ&fals
eF'/%*separatorGFH/%)stretchyGFH/%*symmetricGFH/%(largeopGFH/%.movable
limitsGFH/%'accentGFH/%'lspaceGQ&0.0emF'/%'rspaceGFW-I#mnGF$6$Q\"1F'FA
-Fen6$Q\"2F'FA/%1superscriptshiftGQ\"2F'/%/subscriptshiftGQ\"0F'F+-F#6
%-F,6%Q$sinF'/F0FHFA-F;6-Q0⁡F'FAFFFIFKFMFOFQFSFUFX-I(mfe
ncedGF$6$-F#6%F+-F#6#-I%msupGF$6%-F,6%Q\"xF'F/F2Fhn/F\\oF`oF+FAF+-I'ms
paceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.3emF'/%&depthGF]q/%*linebreak
GQ%autoF'-F;6/Q0ⅆF'F>FAFCFFFIFKFMFOFQFSFUFXFdpF+" }{TEXT
 227 19 "   with   n = 20.  " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "f:=x->sin(x^2);" }{TEXT 227 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "middlesum(f(x),x=1..2,20);" }}}{PARA 0 "" 0 "" {TEXT 
227 120 "This command only shows the expression. To calculate its valu
e - approximate value of the integral -  use command evalf:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Mid:=evalf(%);" }}}{PARA 0 "" 0 "" 
{TEXT 227 120 "To estimate how good this approximation is, estimate th
e error.The formula for error estimate in the Midpoint method is " }
{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true
\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mfenced(
Typesetting:-mi(\"E\", italic = \"true\", mathvariant = \"italic\"), m
athvariant = \"normal\", Typesetting:-msemantics = \"abs\", open = \"&
verbar;\", close = \"|\", Typesetting:-msemantics = \"abs\"), T
ypesetting:-mo(\"=\", mathvariant = \"normal\", fence = \"false\", sep
arator = \"false\", stretchy = \"false\", symmetric = \"false\", large
op = \"false\", movablelimits = \"false\", accent = \"false\", lspace \+
= \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mfrac(Types
etting:-mrow(Typesetting:-mi(\"K\", italic = \"true\", mathvariant = \+
\"italic\"), Typesetting:-mo(\"⁢\", mathvariant = \"nor
mal\", fence = \"false\", separator = \"false\", stretchy = \"false\",
 symmetric = \"false\", largeop = \"false\", movablelimits = \"false\"
, accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typeset
ting:-mrow(Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Ty
pesetting:-mi(\"b\", italic = \"true\", mathvariant = \"italic\"), Typ
esetting:-mo(\"−\", mathvariant = \"normal\", fence = \"false\",
 separator = \"false\", stretchy = \"false\", symmetric = \"false\", l
argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp
ace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mi(\"a
\", italic = \"true\", mathvariant = \"italic\")), mathvariant = \"nor
mal\"), Typesetting:-mn(\"3\", mathvariant = \"normal\"), superscripts
hift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant =
 \"italic\")), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true
\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mn(\"24
\", mathvariant = \"normal\"), Typesetting:-mo(\"⁢\", m
athvariant = \"normal\", fence = \"false\", separator = \"false\", str
etchy = \"false\", symmetric = \"false\", largeop = \"false\", movable
limits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \+
\"0.0em\"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\"n\",
 italic = \"true\", mathvariant = \"italic\"), Typesetting:-mn(\"2\", \+
mathvariant = \"normal\"), superscriptshift = \"0\")), Typesetting:-mi
(\"\", italic = \"true\", mathvariant = \"italic\")), Typesetting:-mi(
\"\", italic = \"true\", mathvariant = \"italic\")), linethickness = \+
\"1\", denomalign = \"center\", numalign = \"center\", bevelled = \"fa
lse\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"ital
ic\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#mi
GF$6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6%-I(mfencedGF$
6(-F,6%Q\"EF'F/F2/F3Q'normalF'/I+msemanticsGF$Q$absF'/%%openGQ)&verbar
;F'/%&closeGFDF?-I#moGF$6-Q\"=F'F=/%&fenceGQ&falseF'/%*separatorGFM/%)
stretchyGFM/%*symmetricGFM/%(largeopGFM/%.movablelimitsGFM/%'accentGFM
/%'lspaceGQ,0.2777778emF'/%'rspaceGFfn-I&mfracGF$6(-F#6&-F,6%Q\"KF'F/F
2-FH6-Q1⁢F'F=FKFNFPFRFTFVFX/FenQ&0.0emF'/FhnFeo-F#6#-I%
msupGF$6%-F86$-F#6%-F,6%Q\"bF'F/F2-FH6-Q(−F'F=FKFNFPFRFTFVFX/Fen
Q,0.2222222emF'/FhnFgp-F,6%Q\"aF'F/F2F=-I#mnGF$6$Q\"3F'F=/%1superscrip
tshiftGQ\"0F'F+-F#6%F+-F#6&-F]q6$Q#24F'F=Fao-F#6#-Fjo6%-F,6%Q\"nF'F/F2
-F]q6$Q\"2F'F=F`qF+F+/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%
)numalignGFir/%)bevelledGFMF+" }{TEXT 227 8 "  where " }{TEXT 220 1 "K
" }{TEXT 227 58 " is a boundary for the second derivative of the funct
ion  " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"f\", italic
 = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"
I,TypesettingGI(_syslibGF'6#-I#miGF$6%Q\"fF'/%'italicGQ%trueF'/%,mathv
ariantGQ'italicF'" }{TEXT 227 10 ". To find " }{TEXT 221 1 "K" }{TEXT 
227 28 ", we may draw the graph of  " }{TEXT 222 5 "f'' :" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(diff(f(x),x,x),x=1..2);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 227 13 "Can see that " }{TEXT 223 1 "K" }
{TEXT 227 66 " is less than 11. So, the error of approximation is not \+
more than:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "E:=11/(24*20^
2); evalf(E);" }}}}{PARA 0 "" 0 "" {TEXT 227 0 "" }}{SECT 1 {PARA 212 
"" 0 "" {TEXT 201 16 "Trapezoid method" }}{PARA 0 "" 0 "" {TEXT 227 
107 "Everything like for midpoint, except the command used is trapezoi
d , and the formula for error estimate is " }{XPPEDIT 18 0 "Typesettin
g:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"itali
c\"), Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mi(\"E\", it
alic = \"true\", mathvariant = \"italic\"), mathvariant = \"normal\", \+
Typesetting:-msemantics = \"abs\", open = \"|\", close = \"&ver
bar;\", Typesetting:-msemantics = \"abs\"), Typesetting:-mo(\"=\", mat
hvariant = \"normal\", fence = \"false\", separator = \"false\", stret
chy = \"false\", symmetric = \"false\", largeop = \"false\", movableli
mits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspace
 = \"0.2777778em\"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:
-mi(\"K\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-
mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", \+
separator = \"false\", stretchy = \"false\", symmetric = \"false\", la
rgeop = \"false\", movablelimits = \"false\", accent = \"false\", lspa
ce = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mrow(Typesetting:-ms
up(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"b\", itali
c = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"−\", \+
mathvariant = \"normal\", fence = \"false\", separator = \"false\", st
retchy = \"false\", symmetric = \"false\", largeop = \"false\", movabl
elimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rsp
ace = \"0.2222222em\"), Typesetting:-mi(\"a\", italic = \"true\", math
variant = \"italic\")), mathvariant = \"normal\"), Typesetting:-mn(\"3
\", mathvariant = \"normal\"), superscriptshift = \"0\")), Typesetting
:-mi(\"\", italic = \"true\", mathvariant = \"italic\")), Typesetting:
-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic
\"), Typesetting:-mrow(Typesetting:-mn(\"12\", mathvariant = \"normal
\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", f
ence = \"false\", separator = \"false\", stretchy = \"false\", symmetr
ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent
 = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mr
ow(Typesetting:-msup(Typesetting:-mi(\"n\", italic = \"true\", mathvar
iant = \"italic\"), Typesetting:-mn(\"2\", mathvariant = \"normal\"), \+
superscriptshift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", m
athvariant = \"italic\")), Typesetting:-mi(\"\", italic = \"true\", ma
thvariant = \"italic\")), linethickness = \"1\", denomalign = \"center
\", numalign = \"center\", bevelled = \"false\")), Typesetting:-mi(\"
\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modu
lenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'
/%,mathvariantGQ'italicF'-F#6%-I(mfencedGF$6(-F,6%Q\"EF'F/F2/F3Q'norma
lF'/I+msemanticsGF$Q$absF'/%%openGQ)|F'/%&closeGFDF?-I#moGF$6-Q
\"=F'F=/%&fenceGQ&falseF'/%*separatorGFM/%)stretchyGFM/%*symmetricGFM/
%(largeopGFM/%.movablelimitsGFM/%'accentGFM/%'lspaceGQ,0.2777778emF'/%
'rspaceGFfn-I&mfracGF$6(-F#6&-F,6%Q\"KF'F/F2-FH6-Q1⁢F'F
=FKFNFPFRFTFVFX/FenQ&0.0emF'/FhnFeo-F#6#-I%msupGF$6%-F86$-F#6%-F,6%Q\"
bF'F/F2-FH6-Q(−F'F=FKFNFPFRFTFVFX/FenQ,0.2222222emF'/FhnFgp-F,6%
Q\"aF'F/F2F=-I#mnGF$6$Q\"3F'F=/%1superscriptshiftGQ\"0F'F+-F#6%F+-F#6&
-F]q6$Q#12F'F=Fao-F#6#-Fjo6%-F,6%Q\"nF'F/F2-F]q6$Q\"2F'F=F`qF+F+/%.lin
ethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGFir/%)bevelledGFM
F+" }{TEXT 227 3 ".  " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:x
->sin(x^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "trapezoid(f(
x),x=1..2,10); Trap:=evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "E:=11/(12*20^2);evalf(E);" }}}{PARA 0 "" 0 "" {TEXT 227 0 "" }
}}{SECT 1 {PARA 0 "" 0 "" {TEXT 224 0 "" }{TEXT 201 14 "Simpson method
" }}{PARA 0 "" 0 "" {TEXT 227 55 "Again everything is similar except t
he command used is " }{TEXT 225 7 "simpson" }{TEXT 227 38 ", and the e
rror estimate is different:" }{XPPEDIT 18 0 "Typesetting:-mrow(Typeset
ting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typesetti
ng:-mrow(Typesetting:-mfenced(Typesetting:-mi(\"E\", italic = \"true\"
, mathvariant = \"italic\"), mathvariant = \"normal\", Typesetting:-ms
emantics = \"abs\", open = \"|\", close = \"|\", Typeset
ting:-msemantics = \"abs\"), Typesetting:-mo(\"=\", mathvariant = \"no
rmal\", fence = \"false\", separator = \"false\", stretchy = \"false\"
, symmetric = \"false\", largeop = \"false\", movablelimits = \"false
\", accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778
em\"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mi(\"M\", ita
lic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"&Invisibl
eTimes;\", mathvariant = \"normal\", fence = \"false\", separator = \"
false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fals
e\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\"
, rspace = \"0.0em\"), Typesetting:-mrow(Typesetting:-msup(Typesetting
:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"b\", italic = \"true\", \+
mathvariant = \"italic\"), Typesetting:-mo(\"−\", mathvariant = \+
\"normal\", fence = \"false\", separator = \"false\", stretchy = \"fal
se\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fa
lse\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222
222em\"), Typesetting:-mi(\"a\", italic = \"true\", mathvariant = \"it
alic\")), mathvariant = \"normal\"), Typesetting:-mn(\"5\", mathvarian
t = \"normal\"), superscriptshift = \"0\")), Typesetting:-mi(\"\", ita
lic = \"true\", mathvariant = \"italic\")), Typesetting:-mrow(Typesett
ing:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typesettin
g:-mrow(Typesetting:-mn(\"180\", mathvariant = \"normal\"), Typesettin
g:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false
\", separator = \"false\", stretchy = \"false\", symmetric = \"false\"
, largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+
lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mrow(Typesetting
:-msup(Typesetting:-mi(\"n\", italic = \"true\", mathvariant = \"itali
c\"), Typesetting:-mn(\"4\", mathvariant = \"normal\"), superscriptshi
ft = \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \+
\"italic\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \+
\"italic\")), linethickness = \"1\", denomalign = \"center\", numalign
 = \"center\", bevelled = \"false\")), Typesetting:-mi(\"\", italic = \+
\"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,T
ypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,mathvarian
tGQ'italicF'-F#6%-I(mfencedGF$6(-F,6%Q\"EF'F/F2/F3Q'normalF'/I+msemant
icsGF$Q$absF'/%%openGQ)|F'/%&closeGFDF?-I#moGF$6-Q\"=F'F=/%&fen
ceGQ&falseF'/%*separatorGFM/%)stretchyGFM/%*symmetricGFM/%(largeopGFM/
%.movablelimitsGFM/%'accentGFM/%'lspaceGQ,0.2777778emF'/%'rspaceGFfn-I
&mfracGF$6(-F#6&-F,6%Q\"MF'F/F2-FH6-Q1⁢F'F=FKFNFPFRFTFV
FX/FenQ&0.0emF'/FhnFeo-F#6#-I%msupGF$6%-F86$-F#6%-F,6%Q\"bF'F/F2-FH6-Q
(−F'F=FKFNFPFRFTFVFX/FenQ,0.2222222emF'/FhnFgp-F,6%Q\"aF'F/F2F=-
I#mnGF$6$Q\"5F'F=/%1superscriptshiftGQ\"0F'F+-F#6%F+-F#6&-F]q6$Q$180F'
F=Fao-F#6#-Fjo6%-F,6%Q\"nF'F/F2-F]q6$Q\"4F'F=F`qF+F+/%.linethicknessGQ
\"1F'/%+denomalignGQ'centerF'/%)numalignGFir/%)bevelledGFMF+" }{TEXT 
227 9 "  where  " }{TEXT 226 1 "M" }{TEXT 227 69 "  is a boundary for \+
the fourth derivative of the integrand function. " }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 39 "simpson(f(x),x=1..2,10); Sim:=evalf(%);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(diff(f(x),x$4),x=1..2);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 227 4 "So, " }{XPPEDIT 18 0 "Typeset
ting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"it
alic\"), Typesetting:-mrow(Typesetting:-mi(\"M\", italic = \"true\", m
athvariant = \"italic\"), Typesetting:-mo(\"=\", mathvariant = \"norma
l\", fence = \"false\", separator = \"false\", stretchy = \"false\", s
ymmetric = \"false\", largeop = \"false\", movablelimits = \"false\", \+
accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"
), Typesetting:-mn(\"170\", mathvariant = \"normal\")), Typesetting:-m
i(\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+
modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%tr
ueF'/%,mathvariantGQ'italicF'-F#6%-F,6%Q\"MF'F/F2-I#moGF$6-Q\"=F'/F3Q'
normalF'/%&fenceGQ&falseF'/%*separatorGFB/%)stretchyGFB/%*symmetricGFB
/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/%'lspaceGQ,0.2777778emF'/
%'rspaceGFQ-I#mnGF$6$Q$170F'F>F+" }{TEXT 227 27 " and the error estima
te is:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "E:=170/(180*10^4)
; evalf(%);" }}}{PARA 4 "" 0 "" {TEXT 229 0 "" }}}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2
 33 1 1 }