integral from 0 to sqrt(a of)xe^{x^2}

Lösung

\int_{0}^{a} x e^{x^{2}} d x

\frac{1}{2} (e^{a} - 1)

Schritte zur Lösung

\int_{0}^{a} x e^{x^{2}} d x

Wende U-Substitution an

= \int_{0}^{a} \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{a} e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= \frac{1}{2} [e^{u}]_{0}^{a}

Berechne die Grenzen:

e^{a} - 1

= \frac{1}{2} (e^{a} - 1)

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