r=1+2sin(6θ)
here's a graph of the equation: http://www.wolframalpha.com/input/?i=polar+1%2B2sin(6x)
I don't know how to set up the integral
I don't think that was quite his question!
The area of a circular sector of radius r and angle is [tex]\frac{1}{2}r^2\theta[/itex]. For an "infinitesmal" angle, we can think of the radius of any curve as constant and so the "differential of area", in polar coordinates, is [tex]\frac{1}{2}r^2 d\theta[/itex].
You want .