Question

Let S be the set of points {(r, theta): 2<=r<=6, pi/3 <= theta<= 5pi/6} Find the area of S. Im having trouble with this problem and have been stuck on it for a while. Any help?

Answer 1

5pi/6 - pi/3 = pi/2 so you have 1/4 of a ring. The area of a ring is just the smaller circle subtracted from the larger circle.

So, the area is

1/4 (pi (6^2-2^2))