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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