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Today's calculation of Integral 274

Source: 1981 Tokyo university entrance exam/Humanities

January 23, 2008
calculusintegrationfunctioncalculus computations

Problem Statement

For real constant numbers a, b, c, d, a,\ b,\ c,\ d, consider the function f(x) \equal{} ax^3 \plus{} bx^2 \plus{} cx \plus{} d such that f( \minus{} 1) \equal{} 0,\ f(1) \equal{} 0,\ f(x)\geq 1 \minus{} |x| for ∣x∣≤1. |x|\leq 1. Find f(x) f(x) for which \int_{ \minus{} 1}^1 \{f'(x) \minus{} x\}^2\ dx　is minimized.
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