find the area of double integral over R dxdy enclosed by the polar curve r(t) = 2 + sin (10t) where t ranges from 0 to 2pi.

i used the method integral (magnitude of r'(t)) over t= 0 to 2pi..

but it was wrong..may i know why?

Results 1 to 4 of 4

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

- Joined
- Aug 2009
- Posts
- 639

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

- Joined
- Mar 2010
- Posts
- 1,028
- Thanks
- 266

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

- Joined
- Aug 2009
- Posts
- 639

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

- Joined
- Mar 2010
- Posts
- 1,028
- Thanks
- 266

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