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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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)