Question

A function f : R® R satisfies f(x+y) = f(x) + f(y) for all x,y Î R and is continuous throughout the domain. If I1 + I2 + I3 + I+ I5 = 450, where In = n.0òn f(x) dx. Find f(x).

Joshi sir comment

according to the given condition f(nx) = n f(x)

0òn f(x) dx

consider x = ny so this integration will become 0ò1 f(ny) ndy = n0ò1 f(y) dy = n2 0ò1 f(x) dx

now by using these conditions I1 = 13 0ò1 f(x) dx similarly others 

put these values and get the answer

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