# How do you find the area of the region bounded by the polar curve #r^2=4cos(2theta)# ?

##### 1 Answer

The first thing to remember that an integral is a way to add up an infinite number of areas. For rectangular coordinates (

literally means "let's find the area of an infinite numbers of rectangles between

Polar coordinates, though it seems more complicated, follows the same general pattern. The big difference is that we're not dealing with rectangles. We are dealing with sectors of a circle. Also known as pizza slices.

The area of a single pizza slice of a circle is

(remember this particular area formula only works if

So the area of an infinite number of "pizza slices" is

which literally means "let's find the area of an infinite number of pizza slices between *r* equals the radius of each pizza slice.

Now for your specific problem, we substitute

Now we have to determine a suitable

First we remember what a lemniscate looks like.

The

It looks like the simplest thing to do is to have our angle go from

So...