What is the integral from 0 to infinity of 5ye^{-5y} ?

The integral from 0 to infinity of 5ye^{-5y} is 1/5

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integral from 0 to infinity of 5ye^{-5y}

\int_{0}^{\infty} 5 y e^{- 5 y} d y

\frac{1}{5}

Solution steps

\int_{0}^{\infty} 5 y e^{- 5 y} d y

Compute the indefinite integral:

\int 5 y e^{- 5 y} d y = - e^{- 5 y} y - \frac{1}{5} e^{- 5 y} + C

Compute the boundaries:

\int_{0}^{\infty} 5 y e^{- 5 y} d y = 0 - (- \frac{1}{5})

= 0 - (- \frac{1}{5})

Simplify

= \frac{1}{5}

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What is the integral from 0 to infinity of 5ye^{-5y} ?
The integral from 0 to infinity of 5ye^{-5y} is 1/5