integral from 0 to 120 of 3-3e^{-0.15t}

解

\int_{0}^{120} 3 - 3 e^{- 0.15 t} d t

\frac{20}{e ^{18}} + 340

十進法表記

340.00000 \dots

解答ステップ

\int_{0}^{120} 3 - 3 e^{- 0.15 t} 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_{0}^{120} 3 d t - \int_{0}^{120} 3 e^{- 0.15 t} d t

\int_{0}^{120} 3 d t = 360

\int_{0}^{120} 3 e^{- 0.15 t} d t = 20 (1 - \frac{1}{e ^{18}})

= 360 - 20 (1 - \frac{1}{e ^{18}})

簡素化

360 - 20 (1 - \frac{1}{e ^{18}}) : \frac{20}{e ^{18}} + 340

= \frac{20}{e ^{18}} + 340