integral from-pi/4 to pi/4 of sin(x)-e^x

解

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin (x) - e^{x} d x

- (e^{\frac{π}{4}} - \frac{1}{e ^{\frac{π}{4}}})

十進法表記

- 1.73734 \dots

解答ステップ

\int_{- \frac{π}{4}}^{\frac{π}{4}} 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_{- \frac{π}{4}}^{\frac{π}{4}} sin (x) d x - \int_{- \frac{π}{4}}^{\frac{π}{4}} e^{x} d x

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin (x) d x = 0

\int_{- \frac{π}{4}}^{\frac{π}{4}} e^{x} d x = e^{\frac{π}{4}} - \frac{1}{e ^{\frac{π}{4}}}

= 0 - (e^{\frac{π}{4}} - \frac{1}{e ^{\frac{π}{4}}})

簡素化

= - (e^{\frac{π}{4}} - \frac{1}{e ^{\frac{π}{4}}})