What is the integral from 0 to infinity of ye^{-3y} ?

The integral from 0 to infinity of ye^{-3y} is 1/9

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 ye^{-3y}

\int_{0}^{\infty} y e^{- 3 y} d y

\frac{1}{9}

Decimal Notation

0.11111 \dots

Solution steps

\int_{0}^{\infty} y e^{- 3 y} d y

Compute the indefinite integral:

\int y e^{- 3 y} d y = \frac{1}{9} (- 3 e^{- 3 y} y - e^{- 3 y}) + C

Compute the boundaries:

\int_{0}^{\infty} y e^{- 3 y} d y = 0 - (- \frac{1}{9})

= 0 - (- \frac{1}{9})

Simplify

= \frac{1}{9}

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{3} + 1})

\int cos (mπ x) d x

f (x) = 20 x^{\frac{1}{2}} - \frac{1}{2} x^{20}

12 t^{3} - t^{2}

\frac{d}{d x} (2 x - \frac{4}{x})

What is the integral from 0 to infinity of ye^{-3y} ?
The integral from 0 to infinity of ye^{-3y} is 1/9