What is the integral from 0 to infinity of ye^{-3y} ?

The integral from 0 to infinity of ye^{-3y} is 1/9

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integral from 0 to infinity of ye^{-3y}

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

\frac{1}{9}

Decimal

0.11111 \dots

Solution steps

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

Compute the indefinite integral:

\int y e^{- 3 y} d y = \frac{1}{9} (- 3 e^{- 3 y} y - e^{- 3 y}) + C

Compute the boundaries:

\int_{0}^{\infty} y e^{- 3 y} d y = 0 - (- \frac{1}{9})

= 0 - (- \frac{1}{9})

Simplify

= \frac{1}{9}

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What is the integral from 0 to infinity of ye^{-3y} ?
The integral from 0 to infinity of ye^{-3y} is 1/9