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?
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.