Today's calculation of Integral 510
Source: 1977 Yokahama National University entrance exam/Engineering
December 2, 2009
calculusintegrationtrigonometryfunctionderivativecalculus computations
Problem Statement
(1) Evaluate \int_0^{\frac{\pi}{2}} (x\cos x\plus{}\sin ^ 2 x)\sin x\ dx.
(2) For f(x)\equal{}\int_0^x e^t\sin (x\minus{}t)\ dt, find f''(x)\plus{}f(x).