numerical integration and solving for limit

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I have the following equation:
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?

Accepted Answer

Star Strider
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.
Star Strider
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.

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