Chapter 14.3, Problem 30E

Converting to Polar Coordinates:

In Exercises 29–-32, use polar coordinates to set up and evaluate the double integral

${\displaystyle {\int }_R{\displaystyle \int f(x,y)dA}}$

$\begin{array}{l}f(x,y)=e^{\raisebox{1ex}{$-(x^2+y^2)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\\ R:x^2+y^2\le 25,x\ge 0\end{array}$