Mathematics

Problem

For

0\le \theta\le \pi

, Curve C is given by

r=\dfrac{\theta}{\pi}

and Curve D by

r=\dfrac12

. Find the value

\theta^*

(

0<\theta^*<\pi

) for which the area swept out by Curve C from

\theta=0

\theta=\theta^*

equals the area swept out by Curve D over the same interval.