MathDB

650

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 650

Source:

9/20/2010
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.
1995 Hitotsubashi University entrance exam/Law, Economics etc.
calculusintegrationalgebrapolynomialcalculus computations