What is the integral from 0 to infinity of 2e^{-x-2y} ?

The integral from 0 to infinity of 2e^{-x-2y} is e^{-x}

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integral from 0 to infinity of 2e^{-x-2y}

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

e^{- x}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= e^{- x}

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What is the integral from 0 to infinity of 2e^{-x-2y} ?
The integral from 0 to infinity of 2e^{-x-2y} is e^{-x}