Ok, i need find the and for the parametric equations.

First, i tried to find from from the range( , )? but the integral is so hard to be solved, i think i get something wrong here.

Then i tried to find it from where and

The integral still owned me, could someone help me or give me some advice?

Btw, do we need to know about the turning points of radial motion ? I think it helps a lot for the integral.