integral from-pi/2 to pi/2 of (cos(x)-5)

解

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x) - 5) d x

2 - 5 π

十進法表記

- 13.70796 \dots

解答ステップ

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 5 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}{2}}^{\frac{π}{2}} cos (x) d x - \int_{- \frac{π}{2}}^{\frac{π}{2}} 5 d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x = 2

\int_{- \frac{π}{2}}^{\frac{π}{2}} 5 d x = 5 π

= 2 - 5 π