Find the total length of the cardioid r=a(1-cos theta)
ds= integral from beta to alpha sqrt[r2 + (dr/d theta)2]dtheta
The Attempt at a Solution
dr=a(sin theta)d theta
ds2=a2(1-cos theta)2d theta2 + a2sin2theta (d theta2), which reduces to:
ds=21/2a(1-cos theta)1/2(d theta)
I'm good up to this point. My book says that the above equation for ds simplifies to:
I don't see how to arrive at this simplification. Can someone please explain? Many thanks.