MathDB

Today's calculation of Integral 27

Source: 1979 Saitama University

May 28, 2005

calculusintegrationtrigonometryquadraticsalgebracalculus computations

Problem Statement

Let

f(x)=t\sin x+(1-t)\cos x\ (0\leqq t\leqq 1)

. Find the maximum and minimum value of the following

P(t)

P(t)=\left\{\int_0^{\frac{\pi}{2}} e^x f(x) dx \right\}\left\{\int_0^{\frac{\pi}{2}} e^{-x} f(x)dx \right\}