Hello, wvlilgurl!
Evaluate the integral by reversing the order of integration.
.$\displaystyle \int^2_0 \int^4_{y^2} y\cos(x^2)\,dx\,dy $ The region is bounded by: .$\displaystyle \begin{array}{c}y\,=\,2\\ y\,=\,0\end{array}\:\text{ and }\:\begin{array}{c}x\,=\,4 \\ x=y^2\end{array}$ Code:

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 4
Reversing the order: .$\displaystyle \begin{array}{c} y \,=\,x^{\frac{1}{2}} \\ y \,=\,0\end{array}\:\text{ and }\:\begin{array}{c}x \,=\,4 \\ x\,=\,0 \end{array}$
The integral becomes: .$\displaystyle \int^4_0 \int^{x^{\frac{1}{2}}}_0 y\cos(x^2)\,dy\,dx$