367

Part of 2008 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 367

Source: 1990 Kogakuin University entrance exam/Architecture, Erectronics

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.

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