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

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

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

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

1

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

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\int_{0}^{1} 2 z d z

\int_{1}^{\infty} \frac{4}{7 x - 1} d x

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