integral from 0 to pi of (3e^x+8sin(x))

解

\int_{0}^{π} (3 e^{x} + 8 sin (x)) d x

3 e^{π} + 13

十進法表記

82.42207 \dots

解答ステップ

\int_{0}^{π} 3 e^{x} + 8 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} 3 e^{x} d x + \int_{0}^{π} 8 sin (x) d x

\int_{0}^{π} 3 e^{x} d x = 3 (e^{π} - 1)

\int_{0}^{π} 8 sin (x) d x = 16

= 3 (e^{π} - 1) + 16

簡素化

3 (e^{π} - 1) + 16 : 3 e^{π} + 13

= 3 e^{π} + 13