Reimann sum and numerical integration
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I am trying to solve the functions below numerically using MATLAB
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/146914/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/146915/image.png)
This is my code where I have used "integral" command to solve for the second integral, while I used Reimann sum to solve for the first. Take for example c=1/128.
x= -1/128:0.0001:1/128;
for j=1:length(x)
den= @(y) pi^2.* sqrt(1- (x(j)+y).^2) .* sqrt(1- y.^2);
fun= @(y) 1./den(y);
ymin= max(-0.999,-0.999-x(j));
ymax= min(0.999,0.999-x(j));
pdfX(j)=integral(fun,ymin,ymax);
end
sum1=0;
for j=1:length(omegat)
func1(j)=pdfX(j)*0.0001;
sum1=sum1+func1(j);
end
F=sum1;
Do you think it is correct? Are there any other ways to make it more accurate?
Thanks
0 Comments
Accepted Answer
Star Strider
on 25 Jan 2015
I would likely use either trapz or cumtrapz to calculate ‘F’, but otherwise I see no problems.
3 Comments
Star Strider
on 25 Jan 2015
F = trapz(x, pdfX)
Avoiding the singularity is likely a good move. I doubt that substituting -0.999 would produce significant error. You might want to experiment with (1-1E-8) instead if you are curious.
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