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119

Part of 2006 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 119

Source: Tokyo Institute of technology entrance exam 1976

7/7/2006
Find the continuous function f(x)f(x) and constant number such that ∫0xf(t) dt=ex−ae2x∫01f(t)e−t dt.\int_{0}^{x}f(t)\ dt=e^{x}-ae^{2x}\int_{0}^{1}f(t)e^{-t}\ dt.
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