What is the integral from 0 to 6 of 80xe^{(-x)/(10)} ?

The integral from 0 to 6 of 80xe^{(-x)/(10)} is 80(-(160)/(e^{3/5)}+100)

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integral from 0 to 6 of 80xe^{(-x)/(10)}

\int_{0}^{6} 80 x e^{\frac{- x}{10}} d x

80 (- \frac{160}{e ^{\frac{3}{5}}} + 100)

Decimal Notation

975.21105 \dots

Solution steps

\int_{0}^{6} 80 x e^{\frac{- x}{10}} d x

Take the constant out:

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

= 80 \cdot \int_{0}^{6} x e^{\frac{- x}{10}} d x

Simplify

= 80 \cdot \int_{0}^{6} e^{- \frac{x}{10}} x d x

Apply Integration By Parts

: [- 10 e^{- \frac{x}{10}} x - \int - 10 e^{- \frac{x}{10}} d x]_{0}^{6}

= 80 [- 10 e^{- \frac{x}{10}} x - \int - 10 e^{- \frac{x}{10}} d x]_{0}^{6}

\int - 10 e^{- \frac{x}{10}} d x = 100 e^{- \frac{x}{10}}

= 80 [- 10 e^{- \frac{x}{10}} x - 100 e^{- \frac{x}{10}}]_{0}^{6}

Compute the boundaries:

- \frac{160}{e ^{\frac{3}{5}}} + 100

= 80 (- \frac{160}{e ^{\frac{3}{5}}} + 100)

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What is the integral from 0 to 6 of 80xe^{(-x)/(10)} ?
The integral from 0 to 6 of 80xe^{(-x)/(10)} is 80(-(160)/(e^{3/5)}+100)