Prove that, for even powers of sine,
∫ 0 π / 2 sin 2 n x d x = 1 ⋅ 3 ⋅ 5 ⋅ ⋅ ⋅ ⋅ ⋅ ( 2 n − 1 ) 2 ⋅ 4 ⋅ 6 ⋅ ⋅ ⋅ ⋅ ⋅ 2 n π 2
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Calculus (MindTap Course List)