What is the integral from 0 to 2 of (x-3)e^{-x} ?

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

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integral from 0 to 2 of (x-3)e^{-x}

\int_{0}^{2} (x - 3) e^{- x} d x

- 2

Solution steps

\int_{0}^{2} (x - 3) e^{- x} d x

Apply Integration By Parts

: [- e^{- x} (x - 3) - \int - e^{- x} d x]_{0}^{2}

= [- e^{- x} (x - 3) - \int - e^{- x} d x]_{0}^{2}

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

= [- e^{- x} (x - 3) - e^{- x}]_{0}^{2}

Expand

- e^{- x} (x - 3) - e^{- x} : - e^{- x} x + 2 e^{- x}

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

Compute the boundaries:

- 2

= - 2

\int_{0}^{2} - 4 x^{4} + 8 x^{3} d x

\int_{0}^{4} (4 x^{3} + \frac{2}{x + 1}) d x

\int_{- 2}^{0} \frac{1}{x ^{2} + 2 x + 2} d x

\int_{- 1}^{0} \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

\int_{1}^{5} x e^{- x} d x

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