# numerical integration and solving for limit

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Benjamin 2019 年 3 月 13 日
コメント済み: Star Strider 2019 年 3 月 18 日
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?

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Star Strider 2019 年 3 月 13 日
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.
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Star Strider 2019 年 3 月 18 日
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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