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Today's calculation of Integral 148

Source: Keio University entrance exam/medical 1975

August 29, 2006
calculusintegrationtrigonometryinductioncalculus computations

Problem Statement

Evaluate ∫0π2sin⁡2nθsin⁡2θ dθ (n=1, 2, ⋯ ).\int_{0}^{\frac{\pi}{2}}\frac{\sin^{2}n\theta}{\sin^{2}\theta}\ d\theta\ (n=1,\ 2,\ \cdots).
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