Chapter 8.7, Problem 22E

To determine

To evaluate: The double integral ${\displaystyle \underset{R}{\iint }f\left(x,y\right)}dA$ where $f\left(x,y\right)=x{e}^{-y^2}$, R is bounded by the lines $x=0$, $x=\sqrt{y}$ and $y=4$.