integral from 0 to 2 of sin(x)+e^x

解

\int_{0}^{2} sin (x) + e^{x} d x

e^{2} - cos (2)

十進法表記

7.80520 \dots

解答ステップ

\int_{0}^{2} sin (x) + e^{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}^{2} sin (x) d x + \int_{0}^{2} e^{x} d x

\int_{0}^{2} sin (x) d x = - cos (2) + 1

\int_{0}^{2} e^{x} d x = e^{2} - 1

= - cos (2) + 1 + e^{2} - 1

簡素化

= e^{2} - cos (2)