428

Part of 2009 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 428

Source: 2009 Kyoto University entrance exam/Humanities, Problem 2

f(x)

be a polynomial and

C

be a real number. Find the

f(x)

C

such that \int_0^x f(y)dy\plus{}\int_0^1 (x\plus{}y)^2f(y)dy\equal{}x^2\plus{}C.

calculusintegrationalgebrapolynomialcalculus computations