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307

Part of 2008 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 307

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

2/26/2008
For real numbers a, b, c a,\ b,\ c, let f(x) \equal{} ax^2 \plus{} bx \plus{} c. Prove that : \int_{ \minus{} 1}^1 (1 \minus{} x^2)\{f'(x)\}^2 dx\leq 6\int_{ \minus{} 1}^1 \{f(x)\}^2 dx.
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