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

The integral from 2 to infinity of x^2e^{-x} is (10)/(e^2)

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integral from 2 to infinity of x^2e^{-x}

\int_{2}^{\infty} x^{2} e^{- x} d x

\frac{10}{e ^{2}}

Decimal

1.35335 \dots

Solution steps

\int_{2}^{\infty} x^{2} e^{- x} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{2}^{\infty} x^{2} e^{- x} d x = 0 - (- \frac{10}{e ^{2}})

= 0 - (- \frac{10}{e ^{2}})

Simplify

= \frac{10}{e ^{2}}

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What is the integral from 2 to infinity of x^2e^{-x} ?
The integral from 2 to infinity of x^2e^{-x} is (10)/(e^2)