integral from 1 to-1 of (6x+5)^2

解

\int_{1}^{- 1} (6 x + 5)^{2} d x

- 74

解答ステップ

\int_{1}^{- 1} (6 x + 5)^{2} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{1} (6 x + 5)^{2} d x

拡張

(6 x + 5)^{2} : 36 x^{2} + 60 x + 25

= - \int_{- 1}^{1} 36 x^{2} + 60 x + 25 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}^{1} 36 x^{2} d x + \int_{- 1}^{1} 60 x d x + \int_{- 1}^{1} 25 d x)

\int_{- 1}^{1} 36 x^{2} d x = 24

\int_{- 1}^{1} 60 x d x = 0

\int_{- 1}^{1} 25 d x = 50

= - (24 + 0 + 50)

簡素化

= - 74