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

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

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

\int_{3}^{\infty} 2 e^{- s t} d t

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

Solution steps

\int_{3}^{\infty} 2 e^{- s t} d t

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

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

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