Chapter 14.5, Problem 30E

To determine

To calculate: A double integral that represents the surface area of $z=f\left(x,y\right)$ lying above the region $R=\left\{\left(x,y\right):x^2+y^2\le 4\right\}$, where surface is $f\left(x,y\right)=e^{-x}\sin y$