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Today's calculation of Integral 268

Source: 1986 Tokyo University entrance exam/Humanities

January 17, 2008
calculusintegrationalgebrapolynomialcalculus computations

Problem Statement

Find the constant numbers u, v, s, t (s<t) u,\ v,\ s,\ t\ (s<t) such that \int_{\minus{}1}^1 f(x)\ dx\equal{}uf(s)\plus{}vf(t) holds for any polynomials f(x)\equal{}ax^3\plus{}bx^2\plus{}cx\plus{}d with the degree of 3 or less than.
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