# Evaluate the integral by reversing the order

• Mar 23rd 2009, 07:21 AM
wvlilgurl
Evaluate the integral by reversing the order
Evaluate the integral by reversing the order of integration.
https://webwork.uncc.edu/webwork2_fi...b1f698fe91.png
• Mar 23rd 2009, 07:55 AM
Soroban
Hello, wvlilgurl!

Quote:

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

• Mar 23rd 2009, 08:11 AM
wvlilgurl
I got that far but I dont know how to integrate it. Thanks!