MathDB
Today's calculation of Integral 333

Source: 1982 Ritsumeikan University entrance exam/Science and Technology

June 3, 2008
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Find the functions f(x), g(x) f(x),\ g(x) such that f(x)\plus{}\int_0^x g(t)\ dt\equal{}\sin x(\cos x\minus{}\sin x),\ \{f'(x)\}^2\plus{}\{g(x)\}^2\equal{}1.