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 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 and for which \int_0^{2\pi} \{f(x) \minus{} S(x)\}^2\ dx is minimized.