Answer
$2a$
Work Step by Step
The length of the curve is given as: $L=\int_{p}^{q}\sqrt{r^2+(\dfrac{dr}{d\theta})^2}d\theta$
Thus, $L=\int_{0}^{\pi} \sqrt{a^2(\dfrac{1-\cos \theta}{2})^2+(\dfrac{asin \theta}{2})^2} d \theta$
Then, we have $L=\dfrac{a}{2} \int_{0}^{\pi} \sqrt {2 (1-\cos \theta)} d\theta$
or, $L =a [2\cos (\theta/2)]_{0}^{\pi}$
Thus, $L=2a$
