Reverse Integration: Solving \int_0^3\int_{y^2}^9 y \cos{x^2} dxdy

[duki]

Homework Statement

Evaluate the integral by reversing the order of integration.

Homework Equations

\int_0^3\int_{y^2}^9 y \cos{x^2} dxdy

The Attempt at a Solution

I want to make sure I'm right so far before going on. I have the reversed limits as:
\sqrt{x} <= y <= 3
0 <= x <= 9

Is this right?

 

[lanedance]

i would try drawing the area, could be wrong, but i think it looks more like:
0 <= y <= \sqrt{x}
0 <= x <= 9

 

[lanedance]

you could also try both integrals to check you get the same area, though i suppose that's why you;re reversing the order in the first place

 

[duki]

Thanks!