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Today's calculation of Integral 115

Source: Chiba University entrance exam 1977

July 7, 2006
calculusintegrationtrigonometrycalculus computations

Problem Statement

Find the value of aa such that ∫0π2(sin⁡x+acos⁡x)3 dx−4aπ−2∫0π2xcos⁡xdx=2.\int_{0}^\frac{\pi}{2}(\sin x+a\cos x)^{3}\ dx-\frac{4a}{\pi-2}\int_{0}^{\frac{\pi}{2}}x\cos x dx=2.
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