integral from 0 to pi/3 of (9x-2)cos(3x)

解

\int_{0}^{\frac{π}{3}} (9 x - 2) cos (3 x) d x

- 2

解答ステップ

\int_{0}^{\frac{π}{3}} (9 x - 2) cos (3 x) d x

拡張

(9 x - 2) cos (3 x) : 9 x cos (3 x) - 2 cos (3 x)

= \int_{0}^{\frac{π}{3}} 9 x cos (3 x) - 2 cos (3 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}^{\frac{π}{3}} 9 x cos (3 x) d x - \int_{0}^{\frac{π}{3}} 2 cos (3 x) d x

\int_{0}^{\frac{π}{3}} 9 x cos (3 x) d x = - 2

\int_{0}^{\frac{π}{3}} 2 cos (3 x) d x = 0

= - 2 - 0

簡素化

= - 2