numerical integration and solving for limit
5 views (last 30 days)
Show older comments
I have the following equation:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/208355/image.png)
g(x) I have as a matrix in an array. It has an x and y column. So I want to take g(x) at a given poin, multiply by 1/x, then integrate, and find where the above statement is true. How can I write a script to solve for X_M for the above integral to be true?
0 Comments
Accepted Answer
Star Strider
on 13 Mar 2019
You have told us nothing about ‘g(x)’. Assuming the integral of ‘g(x)’ is monotonically increasing at least until its integral is equal to 1 (if it’s periodic or has other pecularities, you will need another approach), try this:
x = linspace(1, 10); % ‘x’
y = rand(size(x)); % ‘g(x)’
vint = pi*sqrt(2)/3 * cumtrapz(x, y./x);
X_M = interp1(vint, x, 1);
Experiment to get the result you want.
14 Comments
Star Strider
on 18 Mar 2019
As always, my pleasure! Thank you!
You can always ask a question! (With luck, I will always have an answer.)
The ‘Y_M’ calculation takes the known independent (‘data{1, i}(:,2)’) and dependent (‘data{1, i}(:,4)’) vector values and uses the newly-derived value for ‘X_M(i)’ to calculate (interpolate) the value for ‘Y_M(i)’. The only other additions were to define the figure object and the hold call before the loop, and plot the ‘(X_M(i),Y_M(i))’ values within the loop. The later xlim call simply ‘zooms’ the x-axis slightly to make the plotted ‘+’ markers more visible.
More Answers (0)
See Also
Categories
Find more on Graphics Performance in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!