integral from 0 to pi of-xcos(x)+x

解

\int_{0}^{π} - x cos (x) + x d x

2 + \frac{π ^{2}}{2}

十進法表記

6.93480 \dots

解答ステップ

\int_{0}^{π} - x cos (x) + x d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{0}^{π} x cos (x) d x + \int_{0}^{π} x d x

\int_{0}^{π} x cos (x) d x = - 2

\int_{0}^{π} x d x = \frac{π ^{2}}{2}

= - (- 2) + \frac{π ^{2}}{2}

簡素化

= 2 + \frac{π ^{2}}{2}