304

Part of 2008 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 304

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

\alpha ,\ \beta

be real numbers with

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

\int_0^{\alpha} f(x)\ dx

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