Calculus And Computer Science?

Calculus Level 3

$\large \displaystyle \int_{0}^{\pi} \sin^{20}x \, dx$

The integral above has a closed form. Find this closed form.

Give your answer to 3 decimal places.

Bonus: Compute $\displaystyle \int_{0}^{\pi} \sin^{80}x \, dx$ .

Try a harder version here: Calculus and Computer Science Again?