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Today's calculation of Integral 139

Source: Osaka City University entrance exam 2003

August 13, 2006
calculusintegrationtrigonometryfunctioncalculus computations

Problem Statement

Let a, ba,\ b be real numbers. Evaluate ∫02π(acos⁡x+bsin⁡x)2n dx (n=1, 2, ⋯ ).\int_{0}^{2\pi}(a\cos x+b\sin x)^{2n}\ dx\ (n=1,\ 2,\ \cdots).
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