integral from 0 to y^3 of xe^{-x/y}

Lösung

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

- y^{4} e^{- y^{2}} - y^{2} e^{- y^{2}} + y^{2}

Schritte zur Lösung

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

Wende die partielle Integration an

= [- y e^{- \frac{x}{y}} x - \int - y e^{- \frac{x}{y}} d x]_{0}^{y^{3}}

\int - y e^{- \frac{x}{y}} d x = y^{2} e^{- \frac{x}{y}}

= [- y e^{- \frac{x}{y}} x - y^{2} e^{- \frac{x}{y}}]_{0}^{y^{3}}

Berechne die Grenzen:

- y^{4} e^{- y^{2}} - y^{2} e^{- y^{2}} + y^{2}

= - y^{4} e^{- y^{2}} - y^{2} e^{- y^{2}} + y^{2}

\int \frac{24}{1 - cos ( 3 x )} d x

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