MathDB

278

Part of 2008 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 278

Source: 1982 Doshisya University entrance exam/Engineering

1/23/2008
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.
calculusintegrationtrigonometrylimitcalculus computations