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

The integral from 0 to 2 of x*e^{-x} is -3/(e^2)+1

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

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

- \frac{3}{e ^{2}} + 1

Decimal Notation

0.59399 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int - e^{- x} d x = e^{- x}

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

Compute the boundaries:

- \frac{3}{e ^{2}} + 1

= - \frac{3}{e ^{2}} + 1

x \to 0 + lim (\frac{1}{sin ( x )})

\frac{d}{d x} ((x^{2} + 7) (5 - x))

\int 3 - x^{2} d x

\frac{\partial}{\partial y} (3 y^{2} x + x^{3} + y x^{2})

\frac{d}{d y} (sin (y) - y sin (x))

What is the integral from 0 to 2 of x*e^{-x} ?
The integral from 0 to 2 of x*e^{-x} is -3/(e^2)+1