integral from 0 to y of xe^{-y}

Lösung

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

\frac{y ^{2} e ^{- y}}{2}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{y ^{2}}{2}

= e^{- y} \frac{y ^{2}}{2}

Vereinfache

= \frac{y ^{2} e ^{- y}}{2}

\int_{1}^{e} t ln (t) d t

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