510

Part of 2009 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 510

Source: 1977 Yokahama National University entrance exam/Engineering

(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).

calculusintegrationtrigonometryfunctionderivativecalculus computations