Show that: $$\int\_0^{\pi/2}sin^p\,\theta\;cos^q\,\theta\;d\theta = \frac{\sqrt{\frac{p+1}{2}}\sqrt{\frac{q+1}{2}}}{2\sqrt{\frac{p+q+2}{2}}},\; p,q > -1$$

Here's the question.

[![enter image description here](https://i.stack.imgur.com/NyEF0.jpg)](https://i.stack.imgur.com/NyEF0.jpg)