What is the integral from-1 to 0 of-20xe^{-x} ?

The integral from-1 to 0 of-20xe^{-x} is 20

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integral from-1 to 0 of-20xe^{-x}

\int_{- 1}^{0} - 20 x e^{- x} d x

20

Solution steps

\int_{- 1}^{0} - 20 x e^{- x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 20 \cdot \int_{- 1}^{0} x e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x - \int - e^{- x} d x]_{- 1}^{0}

= - 20 [- e^{- x} x - \int - e^{- x} d x]_{- 1}^{0}

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

= - 20 [- e^{- x} x - e^{- x}]_{- 1}^{0}

Compute the boundaries:

- 1

= - 20 (- 1)

Simplify

= 20

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What is the integral from-1 to 0 of-20xe^{-x} ?
The integral from-1 to 0 of-20xe^{-x} is 20