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Today's Calculation of Integral 51

Source: 1985 The University of Electro-Communications

June 22, 2005
calculusintegrationfunctioncalculus computations

Problem Statement

A function f(x)f(x) satisfies f(x)=f(cx)f(x)=f\left(\frac{c}{x}\right) for some real number c(>1)c(>1) and all positive number xx. If ∫1cf(x)xdx=3\int_1^{\sqrt{c}} \frac{f(x)}{x} dx=3, evaluate ∫1cf(x)xdx\int_1^c \frac{f(x)}{x} dx
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