What is the integral from 0 to infinity of (e^{-x/a})/a ?

The integral from 0 to infinity of (e^{-x/a})/a is 1

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integral from 0 to infinity of (e^{-x/a})/a

\int_{0}^{\infty} \frac{e ^{- \frac{x}{a}}}{a} d x

1

Solution steps

\int_{0}^{\infty} \frac{e ^{- \frac{x}{a}}}{a} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

What is the integral from 0 to infinity of (e^{-x/a})/a ?
The integral from 0 to infinity of (e^{-x/a})/a is 1