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Today's Calculation of Integral 72

Source: 1992 Chiba University

July 16, 2005
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Let f(x)f(x) be a continuous function satisfying f(x)=1+k∫−π2π2f(t)sin⁡(x−t)dt (k:constant number)f(x)=1+k\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} f(t)\sin (x-t)dt\ (k:constant\ number) Find the value of kk for which ∫0πf(x)dx\int_0^{\pi} f(x)dx is maximized.
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