Today's calculation of Integral 565
Source: 2010 Hokkaido University entrance exam/Science, Problem 4
February 25, 2010
calculusintegrationfunctionderivativesymmetrycalculus computations
Problem Statement
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.