point) Evaluate the definite integral $$ \int_{0}^{\pi/2} \sin^5 x \cos^{18} x \, dx $$
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Since the power of $\sin x$ (m=5) is odd, we can use the substitution $u = \cos x$. If $u = \cos x$, then $du = -\sin x \, dx$. We can rewrite $\sin^5 x$ as $\sin^4 x \sin x = (\sin^2 x)^2 \sin x = (1 - \cos^2 x)^2 \sin x$. Show more…
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