What is the integral from 3 to infinity of e^{-x} ?

The integral from 3 to infinity of e^{-x} is 1/(e^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 3 to infinity of e^{-x}

\int_{3}^{\infty} e^{- x} d x

\frac{1}{e ^{3}}

Decimal

0.04978 \dots

Solution steps

\int_{3}^{\infty} e^{- x} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- \frac{1}{e ^{3}})

Simplify

= \frac{1}{e ^{3}}

What is the integral from 3 to infinity of e^{-x} ?
The integral from 3 to infinity of e^{-x} is 1/(e^3)