So I am just fiddling around with converting iterated integral into polar coordinates and I am just a bit stumped with this problem. I think I have figured it out, but I just wanted to make sure:

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles and

After plugging in and I ended up with and . I simplified them so and

After plugging in for I ended up with 24. Have I done this right then? Thanks for all the help!