What is the integral from 0 to infinity of e^{-u} ?

The integral from 0 to infinity of e^{-u} is 1

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integral from 0 to infinity of e^{-u}

\int_{0}^{\infty} e^{- u} d u

1

Solution steps

\int_{0}^{\infty} e^{- u} d u

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} e^{- u} d u = 0 - (- 1)

= 0 - (- 1)

Simplify

= 1

\frac{d y}{d x} = y^{2} - 3 y

t \to 0 lim (\frac{( 3 e ^{t} - 3 )}{t})

\frac{d}{d x} (- \frac{2 x}{( x ^{2} + 3 ) ^{2}})

x \to 0 + lim (\frac{8 x}{sin ( x )})

x \to - 3 lim (∣ x + 3 ∣)

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