how to define a double integral with symbolic upper limits

I want to define a double integral, like this

f(h) = \int_0^h (\int_0^1 xy dx) dy,

where h is a variable.

I try to use command twice: int(int(~,~,~),~,~), but it does not work.

Answer 1

[Walter Roberson]

syms x y h
f(h) = int( int(x*y, x, 0, 1), y, 0, h)

[Yufei Cao]

Dear Walter,

Thanks for your answer.

I find that if the function xy becomes (x.^2 + y.^2).^(1/3), it will not work, since I find matlab int analytically evaluates the first integral and then the second. I would like to define a upper limit integral that can compute numerically when the first integral cannot be evaluated. Thanks in advance.

[Walter Roberson]

matlabFunction(int(int((x.^2 + y.^2)^(1/3), x, 0, 1),0, h),h)

or

f(h) = vpaintegral( vpaintegral(x*y, x, 0, 1), y, 0, h)

[Yufei Cao]

Dear Walter,

Thanks a lot.

I found the first way does not work, see the pic.

But the second one works very well. Thank you very much.