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

The integral from x to infinity of 2e^{-x-y} is 2e^{-2x}

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

\int_{x}^{\infty} 2 e^{- x - y} d y

2 e^{- 2 x}

Solution steps

\int_{x}^{\infty} 2 e^{- x - y} d y

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 2 e^{- 2 x})

Simplify

= 2 e^{- 2 x}

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