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

The integral from 0 to infinity of y^3e^{-y} is 6

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

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

6

Solution steps

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

Compute the indefinite integral:

\int y^{3} e^{- y} d y = - e^{- y} y^{3} - 3 (e^{- y} y^{2} - 2 (- e^{- y} y - e^{- y})) + C

Compute the boundaries:

\int_{0}^{\infty} y^{3} e^{- y} d y = 0 - (- 6)

= 0 - (- 6)

Simplify

= 6

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What is the integral from 0 to infinity of y^3e^{-y} ?
The integral from 0 to infinity of y^3e^{-y} is 6