Chapter 14.3, Problem 31E

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

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

$\begin{array}{l}f(x,y)=\arctan \frac{y}{x}\\ R:x^2+y^2\ge 1,x^2+y^2\le 4,0\le y\le x\end{array}$