college
posted by Laplace transform on .
from 0 to (π/2) ∫(sin^3θ cos^3θ dθ)

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When the sin/cos are in odd powers, use the substitution
cosθdθ=d(sinθ), or
sinθdθ=d(cosθ)
∫sin³θcos³θd&theta (from 0 to π/2)
=∫sin³θ(1sin²θ) (cosθdθ)
=∫(sin³θsin^{5}θ)(d(sinθ)) (from 0 to sin(π/2))
=[sin^{4}θ/4sin^{6}θ/6](from 0 to 1)
=1/12