MathDB
Today's calculation of Integral 345

Source: 1969 Kwansai Gakuin University entrance exam/Science

June 15, 2008
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Given a continuous function f(x) f(x) such that \int_0^{2\pi} f(x)\ dx \equal{} 0. Let S(x) \equal{} A_0 \plus{} A_1\cos x \plus{} B_1\sin x, find constant numbers A0, A1 A_0,\ A_1 and B1 B_1 for which \int_0^{2\pi} \{f(x) \minus{} S(x)\}^2\ dx is minimized.