What is the integral from 2 to 3 of x^2e^{-x} ?

The integral from 2 to 3 of x^2e^{-x} is -(17)/(e^3)+(10)/(e^2)

Popular >

integral from 2 to 3 of x^2e^{-x}

\int_{2}^{3} x^{2} e^{- x} d x

- \frac{17}{e ^{3}} + \frac{10}{e ^{2}}

Decimal Notation

0.50697 \dots

Solution steps

\int_{2}^{3} x^{2} e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x^{2} - \int - 2 e^{- x} x d x]_{2}^{3}

= [- e^{- x} x^{2} - \int - 2 e^{- x} x d x]_{2}^{3}

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

= [- e^{- x} x^{2} - (- 2 (- e^{- x} x - e^{- x}))]_{2}^{3}

Simplify

= [- e^{- x} x^{2} + 2 (- e^{- x} x - e^{- x})]_{2}^{3}

Compute the boundaries:

- \frac{17}{e ^{3}} + \frac{10}{e ^{2}}

= - \frac{17}{e ^{3}} + \frac{10}{e ^{2}}

\int_{0}^{5} \frac{1}{5} d x

\int_{0}^{\infty} (\frac{1}{2})^{x} d x

\int_{- \infty}^{1} \frac{1}{x} d x

\int_{0}^{2} 1 - ∣ 1 - x ∣ d x

\int_{0}^{x} cos (x) sin (x) d x

What is the integral from 2 to 3 of x^2e^{-x} ?
The integral from 2 to 3 of x^2e^{-x} is -(17)/(e^3)+(10)/(e^2)