Double integral with variable limit with integrand as an numerical array

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Akshay Tiwari
Akshay Tiwari 2022-11-24
回答： Walter Roberson 2022-11-24
Ran in:
I have integrands as numerical vectors denoting probability density functions as shown in the following equation.
and are numerical vectors of equal size.
I want to double integrate them with a variable limit () on lower integral. In my knowledge, symbolic integrals (e.g. integral2) available in MATLAB don't take numerical vectors. On the other hand I don't know how to use trapz (used for integration of numerical vectors) when the limit is variable. I am showing one of the codes where I failed.
f1 = 1:100;
f2 = 1:100;
% Element wise multiplication of f1 and f2 to make them a single vector
F = f1.*f2;
I_in = @(t2) trapz(t2:100,F); % inner integral
I = trapz(60:100, I_in(t2));
Unrecognized function or variable 't2'.
It gives the following error:
Error using trapz
Dimension argument must be a positive integer scalar within indexing range.
Any help in this regards would be greatly appreciated.
  2 个评论
Torsten
Torsten 2022-11-24
According to your notation, f1 and f2 have to be matrices, not vectors because f1 = f1(t1,t2) and f2 = f2(t1,t2).
Akshay Tiwari
Akshay Tiwari 2022-11-24
No, and are vectors. The integral equation is implying that and are integrated when can go from to , and can go from to .

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回答（1 个）

Walter Roberson
Walter Roberson 2022-11-24
Use integral2(). The first set of bounds must be numeric, but the second set of bounds can be function handles.

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