# Pythagorean identities will just have to do

Calculus Level 5

$\large \mathscr{E} = \displaystyle \int_{0}^{\pi/2} \sqrt{1- \sin(2016 x) }\, dx$

Find $$\left \lfloor 1000 \mathscr{E} \right \rfloor$$.

Bonus: Make and prove generalization for $$\displaystyle \int_{0}^{\pi/2} \sqrt{1- \sin(12n x) }\, dx$$, where $$n$$ is a positive integer.

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