What is the integral from 0 to infinity of θe^{-θx} ?

The integral from 0 to infinity of θe^{-θx} is 1

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integral from 0 to infinity of θe^{-θx}

\int_{0}^{\infty} θ e^{- θ x} d x

1

Solution steps

\int_{0}^{\infty} θ e^{- θ x} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

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