565

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 565

Source: 2010 Hokkaido University entrance exam/Science, Problem 4

Prove that f(x)\equal{}\int_0^1 e^{\minus{}|t\minus{}x|}t(1\minus{}t)dt has maximal value at x\equal{}\frac 12.

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