integral from 1 to 6 of (8t^3-6t^{-2})

解

\int_{1}^{6} (8 t^{3} - 6 t^{- 2}) d t

2585

解答ステップ

\int_{1}^{6} 8 t^{3} - 6 t^{- 2} d t

6 t^{- 2} = \frac{6}{t ^{2}}

= \int_{1}^{6} 8 t^{3} - \frac{6}{t ^{2}} d t

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}^{6} 8 t^{3} d t - \int_{1}^{6} \frac{6}{t ^{2}} d t

\int_{1}^{6} 8 t^{3} d t = 2590

\int_{1}^{6} \frac{6}{t ^{2}} d t = 5

= 2590 - 5

簡素化

= 2585