# Math Help - Intergral in Polar Coordinate

1. ## Intergral in Polar Coordinate

I need help solving this problem.

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles $x^2+y^2=144$ and $x^2-12x+y^2=0$

2. Its a good idea to know what these circles look like.
The first is easy, its $x^2+y^2=144$ or r=12, which is a circle of radius 12.
if you add 36 to both sides of the second you get $(x-6)^2+y^2=36$.
Now that's a circle that has diameter 12. It traces from (0,0) to (12,0).
NOW that we know what it looks like we can integrate it from zero to $\pi/2$.
The outer radius is 12 and the inner one is that messy circle which we need to solve for in terms of r.
I would do the cal 3 integral of rdrd $\theta$.

$\pi\biggl({144\over 4}-{36\over 2}\biggr)$.