What is the integral from 0 to 3 of (1-e^{-2x}) ?

The integral from 0 to 3 of (1-e^{-2x}) is 3-(e^6-1)/(2e^6)

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integral from 0 to 3 of (1-e^{-2x})

\int_{0}^{3} (1 - e^{- 2 x}) d x

3 - \frac{e ^{6} - 1}{2 e ^{6}}

Decimal

2.50123 \dots

Solution steps

\int_{0}^{3} 1 - e^{- 2 x} d x

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}^{3} 1 d x - \int_{0}^{3} e^{- 2 x} d x

\int_{0}^{3} 1 d x = 3

\int_{0}^{3} e^{- 2 x} d x = \frac{e ^{6} - 1}{2 e ^{6}}

= 3 - \frac{e ^{6} - 1}{2 e ^{6}}

What is the integral from 0 to 3 of (1-e^{-2x}) ?
The integral from 0 to 3 of (1-e^{-2x}) is 3-(e^6-1)/(2e^6)