Today's calculation of Integral 367
Source: 1990 Kogakuin University entrance exam/Architecture, Erectronics
July 26, 2008
calculusintegrationtrigonometrycalculus computations
Problem Statement
Let f(x)\equal{}x^2\plus{}\int_0^1 xf(t)\ dt\plus{}\int_{\minus{}1}^2 f(t)\ dt.
Evaluate \int_0^{\frac{\pi}{2}} f(x\plus{}\sin x)\ dx.