Evaluating Double Integrals of Odd and Even Functions on a Disk

[ChiefKeeper92]

Homework Statement

Suppose f : ℝ→ℝ and g : ℝ →ℝ are continuous. Suppose that f is odd and g is even. Define h(x,y) : f(x)*g(y).
Let D be a disk centered at the origin in the plane. What is

∫∫h(x,y)dA?
D

The Attempt at a Solution

I know there's probably a trick to it. Is it 0 because h becomes odd over a disk that is symmetrical to the origin?

 

[Dick]

Yes, that's basically it. Set it up as a dx*dy integral with limits if you want to show it explicitly.

 

[Dick]

#Error

The problem posted was to evaluate the integral of h(x,y) over a disk D centered on the origin, where h(x,y)=f(x)g(y), f is an even function, g is odd.