What is the integral from 0 to 60 of 5-5e^{-0.2t} ?

The integral from 0 to 60 of 5-5e^{-0.2t} is (25)/(e^{12)}+275

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integral from 0 to 60 of 5-5e^{-0.2t}

\int_{0}^{60} 5 - 5 e^{- 0.2 t} d t

\frac{25}{e ^{12}} + 275

Decimal

275.00015 \dots

Solution steps

\int_{0}^{60} 5 - 5 e^{- 0.2 t} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{60} 5 d t - \int_{0}^{60} 5 e^{- 0.2 t} d t

\int_{0}^{60} 5 d t = 300

\int_{0}^{60} 5 e^{- 0.2 t} d t = 25 (1 - \frac{1}{e ^{12}})

= 300 - 25 (1 - \frac{1}{e ^{12}})

Simplify

300 - 25 (1 - \frac{1}{e ^{12}}) : \frac{25}{e ^{12}} + 275

= \frac{25}{e ^{12}} + 275

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What is the integral from 0 to 60 of 5-5e^{-0.2t} ?
The integral from 0 to 60 of 5-5e^{-0.2t} is (25)/(e^{12)}+275