MathDB
Today's calculation of Integral 766

Source: 1993 National Defence Medical College

November 16, 2011
calculusintegrationfunctiontrigonometryinequalitiescalculus computations

Problem Statement

Let f(x)f(x) be a continuous function defined on 0≤x≤π0\leq x\leq \pi and satisfies f(0)=1f(0)=1 and
{∫0π(sin⁡x+cos⁡x)f(x)dx}2=π∫0π{f(x)}2dx.\left\{\int_0^{\pi} (\sin x+\cos x)f(x)dx\right\}^2=\pi \int_0^{\pi}\{f(x)\}^2dx.
Evaluate ∫0π{f(x)}3dx.\int_0^{\pi} \{f(x)\}^3dx.
Back to ProblemsView on AoPS