# Reversing Integration

1. Apr 1, 2009

### duki

1. The problem statement, all variables and given/known data

Evaluate the integral by reversing the order of integration.

2. Relevant equations

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

3. 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?

2. Apr 2, 2009

### lanedance

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

3. Apr 2, 2009

### lanedance

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

4. Apr 2, 2009

Thanks!