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Today's calculation of Integral 702

Source: 1979 Nagoya University entrance exam/Science

June 3, 2011
calculusintegrationfunctioncalculus computations

Problem Statement

f(x)f(x) is a continuous function defined in x>0x>0. For all a, b (a>0, b>0)a,\ b\ (a>0,\ b>0), if ∫abf(x) dx\int_a^b f(x)\ dx is determined by only ba\frac{b}{a}, then prove that f(x)=cx (c:constant).f(x)=\frac{c}{x}\ (c: constant).
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