What is the integral from 0 to infinity of 10e^{-2x-3y} ?

The integral from 0 to infinity of 10e^{-2x-3y} is 10/3 e^{-2x}

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integral from 0 to infinity of 10e^{-2x-3y}

\int_{0}^{\infty} 10 e^{- 2 x - 3 y} d y

\frac{10}{3} e^{- 2 x}

Solution steps

\int_{0}^{\infty} 10 e^{- 2 x - 3 y} d y

Compute the indefinite integral:

\int 10 e^{- 2 x - 3 y} d y = - \frac{10}{3} e^{- 2 x - 3 y} + C

Compute the boundaries:

\int_{0}^{\infty} 10 e^{- 2 x - 3 y} d y = 0 - (- \frac{10}{3} e^{- 2 x})

= 0 - (- \frac{10}{3} e^{- 2 x})

Simplify

= \frac{10}{3} e^{- 2 x}

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What is the integral from 0 to infinity of 10e^{-2x-3y} ?
The integral from 0 to infinity of 10e^{-2x-3y} is 10/3 e^{-2x}