Area with Polar Coordinates

In this part we are going to look at areas enclosed via polar curves.  Note also that we said "enclosed by" in place of "under" as we usually have in these problems.  These problems work a little in a different way in polar coordinates.  Here is a drawing of what the area that we'll be finding in this part looks like.

We'll be searching for the shaded area in the sketch above.  The formula for finding this area is as follow:

A = ∫^β_α ½ r² dθ

Note: We use r in the integral instead of f (θ) so make sure and substitute as per when doing the integral.