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

The integral from 0 to 2 of x^2e^{-x} is -(10)/(e^2)+2

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integral from 0 to 2 of x^2e^{-x}

\int_{0}^{2} x^{2} e^{- x} d x

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

Decimal

0.64664 \dots

Solution steps

\int_{0}^{2} x^{2} e^{- x} d x

Apply Integration By Parts

= [- e^{- x} x^{2} - \int - 2 e^{- x} x d x]_{0}^{2}

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

= [- e^{- x} x^{2} - (- 2 (- e^{- x} x - e^{- x}))]_{0}^{2}

Simplify

= [- e^{- x} x^{2} + 2 (- e^{- x} x - e^{- x})]_{0}^{2}

Compute the boundaries:

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

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

\int - 2^{x} d x

e x p an d (x^{3} + 1) (x^{2} + x + 1)

\frac{d}{d x} (\frac{5}{3 x ^{2}})

x \to 0 + lim ((tan (4 x))^{x})

d er i v a t i v e \frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}

What is the integral from 0 to 2 of x^2e^{-x} ?
The integral from 0 to 2 of x^2e^{-x} is -(10)/(e^2)+2