What is the integral from 0 to infinity of e^{-y}y^2 ?

The integral from 0 to infinity of e^{-y}y^2 is 2

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integral from 0 to infinity of e^{-y}y^2

\int_{0}^{\infty} e^{- y} y^{2} d y

2

Solution steps

\int_{0}^{\infty} e^{- y} y^{2} d y

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} e^{- y} y^{2} d y = 0 - (- 2)

= 0 - (- 2)

Simplify

= 2

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What is the integral from 0 to infinity of e^{-y}y^2 ?
The integral from 0 to infinity of e^{-y}y^2 is 2