integral from-1 to 0 of 2x-e^x

解

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

\frac{1}{e} - 2

十進法表記

- 1.63212 \dots

解答ステップ

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

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

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

= - 1 - (1 - \frac{1}{e})

簡素化

= \frac{1}{e} - 2