# Thread: Evaluate the integral by reversing the order

1. ## Evaluate the integral by reversing the order

Evaluate the integral by reversing the order of integration.

2. Hello, wvlilgurl!

Evaluate the integral by reversing the order of integration.

. $\int^2_0 \int^4_{y^2} y\cos(x^2)\,dx\,dy$
The region is bounded by: . $\begin{array}{c}y\,=\,2\\ y\,=\,0\end{array}\:\text{ and }\:\begin{array}{c}x\,=\,4 \\ x=y^2\end{array}$
Code:
          |
|             *
2 +         *
|     *:::|
|  *::::::|
|*::::::::|
|:::::::::|
- - * - - - - * - - -
|         4

Reversing the order: . $\begin{array}{c} y \,=\,x^{\frac{1}{2}} \\ y \,=\,0\end{array}\:\text{ and }\:\begin{array}{c}x \,=\,4 \\ x\,=\,0 \end{array}$

The integral becomes: . $\int^4_0 \int^{x^{\frac{1}{2}}}_0 y\cos(x^2)\,dy\,dx$

3. I got that far but I dont know how to integrate it. Thanks!