Quote by Andrew123
1. The problem statement, all variables and given/known data
ok change the region R = { (x,y)  1 <= X^2 + y^2 <= 4 , 0 <= y <= x } to polar region and perform the double integral over region R of z=arctan(y/x)dA
2. Relevant equations
r^2 = x^2 + y^2, x = r*sin(@), y = r * cos (@)
3. The attempt at a solution
i got R = { (rcos(@), rsin(@)  1 <= r <= 2 , 0 <= @ <= pi/4 }
and 3/8 * pi ^2 answer in back of book is 3/64 * pi ^2
thankyou for your time!

You've correctly converted to polar coordinates and found the limits of integration, but you somehow made a mistake evaluating the integral...Did you by chance forget that you are integrating the function [itex]\tan^{1}\left(\frac{y}{x}\right)=\theta[/itex] over this region, andf just find the area of the region instead?