Double integral with variable limit with integrand as an numerical array

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.

[Torsten]

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]

No, and are vectors. The integral equation is implying that and are integrated when can go from to , and can go from to .

Answer 1

[Walter Roberson]

Use integral2(). The first set of bounds must be numeric, but the second set of bounds can be function handles.