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

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

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

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

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

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

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

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