Q:

Area of polar coordinate $r = e^{- \theta/4}$

$$r = e^{- \theta/4}$$
$$\pi /2 \leq \theta \leq \pi$$
I know the formula is 
$$\int_a^b \frac{1}{2} r^2 d\theta$$
$$\int_{\pi/2}^{\pi} \frac{1}{2} (e^{- \theta/4})^2 d\theta$$
From here I cannot figure out an easy way to integrate this.

A:

Note that $(e^{-\theta/4})^2=e^{-\theta/2}$.  It is a special case of the general exponential rule $(a^b)^c=a^{bc}$.

