What is the integral from 3 to infinity of e^{-x/2} ?

The integral from 3 to infinity of e^{-x/2} is 2/(e^{3/2)}

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integral from 3 to infinity of e^{-x/2}

\int_{3}^{\infty} e^{- \frac{x}{2}} d x

\frac{2}{e ^{\frac{3}{2}}}

Decimal

0.44626 \dots

Solution steps

\int_{3}^{\infty} e^{- \frac{x}{2}} d x

Compute the indefinite integral:

\int e^{- \frac{x}{2}} d x = - 2 e^{- \frac{x}{2}} + C

Compute the boundaries:

\int_{3}^{\infty} e^{- \frac{x}{2}} d x = 0 - (- \frac{2}{e ^{\frac{3}{2}}})

= 0 - (- \frac{2}{e ^{\frac{3}{2}}})

Simplify

= \frac{2}{e ^{\frac{3}{2}}}

What is the integral from 3 to infinity of e^{-x/2} ?
The integral from 3 to infinity of e^{-x/2} is 2/(e^{3/2)}