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

The integral from 0 to infinity of e^{-y}y is 1

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 e^{-y}y

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

1

Solution steps

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

Compute the indefinite integral:

\int e^{- y} y d y = - e^{- y} y - e^{- y} + C

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

\int_{0}^{4} (x^{2} - 2 x + 1) d x

\int_{- 2}^{2} (17 - ∣ x ∣^{3}) d x

\int_{1}^{5} x^{2} - x - 6 d x

\int_{1}^{8} \frac{4}{3} x^{\frac{1}{3}} d x

\int_{0}^{1} (5 x^{2} - 8 x + 6) d x

What is the integral from 0 to infinity of e^{-y}y ?
The integral from 0 to infinity of e^{-y}y is 1