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Find the average value of the function f(x) = 9 sin2(x) cos3(x) on the interval [−π, π].

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\displaystyle\frac1{\pi-(-\pi)}\int_(-\pi)^\pi9\sin^2x\cos^3x\,\mathrm dx

=\displaystyle\frac9{2\pi}\int_(-\pi)^\pi\sin^2x(1-\sin^2x)\cos x\,\mathrm dx

=\displaystyle\frac9{2\pi}\int_0^0 y^2(1-y^2)\,\mathrm dy

where we let
y=\sin x. The remaining integral reduces to 0.
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