What is the integral from 4 to infinity of e^{-x/5} ?

The integral from 4 to infinity of e^{-x/5} is 5/(e^{4/5)}

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integral from 4 to infinity of e^{-x/5}

\int_{4}^{\infty} e^{- \frac{x}{5}} d x

\frac{5}{e ^{\frac{4}{5}}}

Decimal

2.24664 \dots

Solution steps

\int_{4}^{\infty} e^{- \frac{x}{5}} d x

Compute the indefinite integral:

\int e^{- \frac{x}{5}} d x = - 5 e^{- \frac{x}{5}} + C

Compute the boundaries:

\int_{4}^{\infty} e^{- \frac{x}{5}} d x = 0 - (- \frac{5}{e ^{\frac{4}{5}}})

= 0 - (- \frac{5}{e ^{\frac{4}{5}}})

Simplify

= \frac{5}{e ^{\frac{4}{5}}}

What is the integral from 4 to infinity of e^{-x/5} ?
The integral from 4 to infinity of e^{-x/5} is 5/(e^{4/5)}