integral from-infinity to 0 of xe^{ax}

Lösung

\int_{- \infty}^{0} x e^{a x} d x

- \frac{1}{a ^{2}}

Schritte zur Lösung

\int_{- \infty}^{0} x e^{a x} d x

Berechne das unbestimmte Integral:

\int x e^{a x} d x = e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}} + C

Berechne die Grenzen:

\int_{- \infty}^{0} x e^{a x} d x = - \frac{1}{a ^{2}} - 0

= - \frac{1}{a ^{2}} - 0

Vereinfache

= - \frac{1}{a ^{2}}

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