# Higher powers

Calculus Level 5

$\large \mathscr{E} = \displaystyle \int_{-\pi/2}^{0} \cos^{21}(x) \sin^{17}(x) \, dx$

If $$\mathscr{E}$$ can be expressed in the form $$- \dfrac{a}{b}$$, with $$a$$ and $$b$$ are coprime positive integers, find $$a + b$$.

No calculators allowed.

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