I think the correct formula is .

To do the integral, you'll need the identity .

To check your answer, the result should be roughly the area of a circle with radius 2, which, of course, is .

- Hollywood

Results 1 to 4 of 4

- April 22nd 2010, 03:30 PM #1

- Joined
- Aug 2009
- Posts
- 639

- April 23rd 2010, 11:01 PM #2

- Joined
- Mar 2010
- Posts
- 1,010
- Thanks
- 252

- April 24th 2010, 03:43 AM #3

- Joined
- Aug 2009
- Posts
- 639

- April 24th 2010, 05:16 PM #4

- Joined
- Mar 2010
- Posts
- 1,010
- Thanks
- 252

If you look at a small piece of the graph, it is a sector of a circle (the shape of a slice of pie). The angle at the origin is , and the radius is . Since the angle at the origin for a whole circle is , our wedge shape is of a circle. Since the area of a circle is , the area of the wedge is . That explains the integrand.

Our curve is traced by going from 0 to , so that explains the limits of integration.

- Hollywood