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## Homework Statement

Evaluate an iterated integral by reversing the order of integration

[tex]\int^1_0\int^1_{y^2} ysin(x^2)dxdy[/tex]

## Homework Equations

## The Attempt at a Solution

I've got that the limits for x is between y^2 and 1, while the limits for y is between 0 and 1. Then I graphed it:

Looking at it from bottom to top, I see that it enters the region at y^2 and leaves at 1. While from left to right, the lowest limit x can be is -1, while the highest is 1. So now I have an integral of [tex]\int^1_{-1}\int^1_{\sqrt{x}}ysin(x^2)dydx[/tex].

Integrating the first part of the equation for y, I get:

[tex]\int^1_{-1} \frac{sin(x^2)}{2}-\frac{xsin(x^2)}{2}dx[/tex]

And it's at this point that I get stuck. I know that I can break up the problem and integrate each part separately, which makes solving the second part easy, since I can just use substitution, but I'm just not sure how to integrate the [tex]\frac{sin(x^2)}{2}[/tex] part. I'm wondering whether this means that I got the limits wrong, or I'm just forgetting trig integrals.