(ii) Find $\int \cos^2(\pi x)\sin(\pi x)dx$.
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Step 1
First, we can use the product-to-sum formula to rewrite the integrand as: cos(x) sin(x) = (1/2)[sin(2x)] So, the integral becomes: ∫ cos(x) sin(x) dx = (1/2) ∫ sin(2x) dx Using the substitution u = 2x, we get: (1/2) ∫ sin(2x) dx = (1/4) ∫ sin(u) Show more…
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