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Today's calculation of Integral 650

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September 20, 2010
calculusintegrationalgebrapolynomialcalculus computations

Problem Statement

Find the values of p, q, r (−1<p<q<r<1)p,\ q,\ r\ (-1<p<q<r<1) such that for any polynomials with degree≤2\leq 2, the following equation holds:
∫−1pf(x) dx−∫pqf(x) dx+∫qrf(x) dx−∫r1f(x) dx=0.\int_{-1}^p f(x)\ dx-\int_p^q f(x)\ dx+\int_q^r f(x)\ dx-\int_r^1 f(x)\ dx=0.
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