Today's calculation of Integral 513
Source: 1968 Kyoto Institute of Technology entrance exam/Fiber and Textile
December 4, 2009
calculusintegrationfunctiontrigonometrycalculus computations
Problem Statement
Find the constants such that a function f(x)\equal{}a\sin x\plus{}b\cos x\plus{}c satisfies the following equation for any real numbers .
5\sin x\plus{}3\cos x\plus{}1\plus{}\int_0^{\frac{\pi}{2}} (\sin x\plus{}\cos t)f(t)\ dt\equal{}f(x).