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Today's calculation of Integral 563

Source: 2010 Tokyo University entrance exam/Humanities, Problem 2

February 25, 2010
calculusintegrationquadraticsfunctioncalculus computations

Problem Statement

Determine the pair of constant numbers a, b, c a,\ b,\ c such that for a quadratic function f(x) \equal{} x^2 \plus{} ax \plus{} b, the following equation is identity with respect to x x. f(x \plus{} 1) \equal{} c\int_0^1 (3x^2 \plus{} 4xt)f'(t)dt .
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