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Today's calculation of Integral 278

Source: 1982 Doshisya University entrance exam/Engineering

January 23, 2008
calculusintegrationtrigonometrylimitcalculus computations

Problem Statement

Find the value of t t such that ∫0π2(sin⁡x+tcos⁡x)dx∫0π2(sin⁡x+tcos⁡x)2dx{ \frac{\int_0^{\frac{\pi}{2}}(\sin x+t\cos x)dx}{\sqrt{\int_0^{\frac{\pi}{2}} (\sin x+t\cos x)^2dx}}} is maximized.
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