integral from 0 to pi of (9e^x+7sin(x))

解

\int_{0}^{π} (9 e^{x} + 7 sin (x)) d x

9 e^{π} + 5

十進法表記

213.26623 \dots

解答ステップ

\int_{0}^{π} 9 e^{x} + 7 sin (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} 9 e^{x} d x + \int_{0}^{π} 7 sin (x) d x

\int_{0}^{π} 9 e^{x} d x = 9 (e^{π} - 1)

\int_{0}^{π} 7 sin (x) d x = 14

= 9 (e^{π} - 1) + 14

簡素化

9 (e^{π} - 1) + 14 : 9 e^{π} + 5

= 9 e^{π} + 5