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Today's calculation of Integral 745

Source: 2011 Toyama University entrance exam

August 29, 2011
calculusintegrationtrigonometrycalculus computations

Problem Statement

When real numbers a, ba,\ b move satisfying ∫0π(acos⁡x+bsin⁡x)2dx=1\int_0^{\pi} (a\cos x+b\sin x)^2dx=1, find the maximum value of ∫0π(ex−acos⁡x−bsin⁡x)2dx.\int_0^{\pi} (e^x-a\cos x-b\sin x)^2dx.
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