echo on
%
% Enter the data, 
% e.g. paste from EXCEL
%
A=[0,5;5,13;10,16;15,17;20,...
      18;25,18;30,17;35,16;...
      40,13;45,10;50,2;]
pause
%
% Pick the x and the y column
%
y=A(:,1)
x=A(:,2)
pause
%
% plot the data, check for errors
%
plot(x,y,'ro')
pause
%
% get help for polyfit
%
pause
help polyfit
%
%
pause
%
% Fit our data x=p(y)
%
pause
p8=polyfit(y,x,8)
pause
%
% need to evaluate the polynomial
% at the given y-data points
%
pause
help polyval
pause
%
% check that things are as desired
% use only few data points now!
% 
pause
yy=[0:10:50]'
pause
xx=polyval(p8,yy)
pause
plot(xx,yy,'b-',x,y,'r*')
%
% Now work with real data, e.g.
% 50 points instead of 5 points
%
yy=[0:1:50]';
xx=polyval(p8,yy);
plot(xx,yy,'b-',x,y,'ro')
pause
%
% Still need to make the grafix
% nicer. Some help pages....
%
pause
help axes
pause
help axis
pause
axis equal
pause
axis([0,50,0,50])
pause
%
% Now back to Riemann sums, but
% working with interpolated data
%
pause
%
% First the volumes. You may want
% to dry-run this with a smaller
% data set first.....
%
pause
vols=pi*xx.^2*1;
vols(1:5)
%
% Volumes of the slices
% Showing oinly the first 5
% The units are (mm)^3
%
pause
masses=vols*0.9/1000;
masses(1:5)
%
% Masses of the slices
% Showing oinly the first 5
% Note the unit conversion
% Now mass in grams
%
pause
inertias=masses.*(xx.^2)/2;
inertias(1:5)
%
% Moments of inertia of slices
% Showing only the first 5
% Units: grams*(mm)^2
%
pause
totiner=sum(inertias)/100
%
% Total moment of inertia
% units converted to g*(cm)^2