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

The integral from x to infinity of e^{-x} is e^{-x}

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integral from x to infinity of e^{-x}

\int_{x}^{\infty} e^{- x} d x

e^{- x}

Solution steps

\int_{x}^{\infty} e^{- x} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- e^{- x})

Simplify

= e^{- x}

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What is the integral from x to infinity of e^{-x} ?
The integral from x to infinity of e^{-x} is e^{-x}