plot a graph showing the convergence of a Integral versus the number of sample points used.

Use Simpson's rule to evaluate the integral of sinx^3 from 0 to 2pi, and plot the convergence of the integral versus the number of sample points used

Answer 1

[Gautham Sholingar]

The following example on file exchange (MATLAB Central) is one implementation of the Simpson's rule integration:

http://www.mathworks.com/matlabcentral/fileexchange/28726-simpson-s-rule-integration?focused=5186784&tab=function

After you download the function, add it to your path and run the following code snippet:

numSamplePoints = 1000;
I = zeros(numSamplePoints,1);
for samplePoints = 1:numSamplePoints
    % samplePoints
    I(samplePoints) = simpsons(@(x)sin(x.^3),0,2*pi,samplePoints);
end
plot(1:samplePoints,I);

This will give you a plot showing the convergence of the integral vs. the number of samples used for the integration as shown below:

Answer 2

[Ali Haider]

write the code to draw convergence curve and draw it?