What is the integral from 0 to infinity of x*e^{-4x} ?

The integral from 0 to infinity of x*e^{-4x} is 1/16

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to infinity of x*e^{-4x}

\int_{0}^{\infty} x \cdot e^{- 4 x} d x

\frac{1}{16}

Solution steps

\int_{0}^{\infty} x e^{- 4 x} d x

Compute the indefinite integral:

\int x e^{- 4 x} d x = \frac{1}{16} (- 4 e^{- 4 x} x - e^{- 4 x}) + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- 4 x} d x = 0 - (- \frac{1}{16})

= 0 - (- \frac{1}{16})

Simplify

= \frac{1}{16}

\int_{0}^{2} \frac{1}{25} y d y

\int_{0}^{4} (x - 6)^{3} d x

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

\int_{0}^{2} 3 x x^{2} + 4 a^{2} d x

\int_{- 2}^{2} 1 - x^{2} d y

What is the integral from 0 to infinity of x*e^{-4x} ?
The integral from 0 to infinity of x*e^{-4x} is 1/16