integral from 0 to 10 of xe^{-x/(14)}

Lösung

\int_{0}^{10} x e^{- \frac{x}{14}} d x

- \frac{336}{e ^{\frac{5}{7}}} + 196

Dezimale

31.51400 \dots

Schritte zur Lösung

\int_{0}^{10} x e^{- \frac{x}{14}} d x

Wende die partielle Integration an

= [- 14 e^{- \frac{x}{14}} x - \int - 14 e^{- \frac{x}{14}} d x]_{0}^{10}

\int - 14 e^{- \frac{x}{14}} d x = 196 e^{- \frac{x}{14}}

= [- 14 e^{- \frac{x}{14}} x - 196 e^{- \frac{x}{14}}]_{0}^{10}

Berechne die Grenzen:

- \frac{336}{e ^{\frac{5}{7}}} + 196

= - \frac{336}{e ^{\frac{5}{7}}} + 196

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