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

Popular >

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}}

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}}

\int_{0}^{\frac{π}{2}} sin^{9} (x) d x

\int_{- 2}^{x} (20 t^{2} - 19 t) d t

\int_{\frac{π}{2}}^{\frac{3 π}{2}} 2 cos (x) d x

\int_{0}^{2} \frac{1}{1 + x ^{4}} d x

\int_{0}^{1} - t d t

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)