What is the integral from 3 to infinity of e^{-x/4} ?

The integral from 3 to infinity of e^{-x/4} is 4/(e^{3/4)}

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integral from 3 to infinity of e^{-x/4}

\int_{3}^{\infty} e^{- \frac{x}{4}} d x

\frac{4}{e ^{\frac{3}{4}}}

Decimal

1.88946 \dots

Solution steps

\int_{3}^{\infty} e^{- \frac{x}{4}} d x

Compute the indefinite integral:

\int e^{- \frac{x}{4}} d x = - 4 e^{- \frac{x}{4}} + C

Compute the boundaries:

\int_{3}^{\infty} e^{- \frac{x}{4}} d x = 0 - (- \frac{4}{e ^{\frac{3}{4}}})

= 0 - (- \frac{4}{e ^{\frac{3}{4}}})

Simplify

= \frac{4}{e ^{\frac{3}{4}}}

What is the integral from 3 to infinity of e^{-x/4} ?
The integral from 3 to infinity of e^{-x/4} is 4/(e^{3/4)}