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

Solution

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

1

Solution steps

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

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

= \int_{0}^{\infty} e^{- y} d y

\int_{0}^{\infty} e^{- y} d y = 1

= 1

y = x^{3} - 5 x, y = 11 x

x \to 8 lim (\frac{\frac{8}{x} - 1}{x - 8})

\frac{d}{d x} (x^{\frac{4}{5}} (x - 9)^{2})

e^{- x}

x \to 8 lim (\frac{1}{x - 8})

What is the integral from 0 to infinity of integral from 0 to infinity of e^{-x-y} ?
The integral from 0 to infinity of integral from 0 to infinity of e^{-x-y} is 1