MathDB
Today's calculation of Integral 304

Source: 2008 Tokyo University entrance exam/Humanities, Problem 1

February 25, 2008
calculusintegrationcalculus computations

Problem Statement

Let α, β \alpha ,\ \beta be real numbers with 0≤α≤β 0\leq \alpha \leq \beta and f(x)\equal{}x^2\minus{}(\alpha \plus{}\beta)x\plus{}\alpha \beta such that \int_{\minus{}1}^1 f(x)\ dx\equal{}1. Find the maximum value of ∫0αf(x) dx \int_0^{\alpha} f(x)\ dx.
Back to ProblemsView on AoPS