integral from 0 to pi of (5e^x+5sin(x))

解

\int_{0}^{π} (5 e^{x} + 5 sin (x)) d x

5 e^{π} + 5

十進法表記

120.70346 \dots

解答ステップ

\int_{0}^{π} 5 e^{x} + 5 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} 5 e^{x} d x + \int_{0}^{π} 5 sin (x) d x

\int_{0}^{π} 5 e^{x} d x = 5 (e^{π} - 1)

\int_{0}^{π} 5 sin (x) d x = 10

= 5 (e^{π} - 1) + 10

簡素化

5 (e^{π} - 1) + 10 : 5 e^{π} + 5

= 5 e^{π} + 5