integral from 0 to 3 of 6xe^{x^2}

Lösung

\int_{0}^{3} 6 x e^{x^{2}} d x

3 (e^{9} - 1)

Dezimale

24306.25178 \dots

Schritte zur Lösung

\int_{0}^{3} 6 x e^{x^{2}} d x

Entferne die Konstante:

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

= 6 \cdot \int_{0}^{3} x e^{x^{2}} d x

Wende U-Substitution an

= 6 \cdot \int_{0}^{9} \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= 6 \cdot \frac{1}{2} \cdot \int_{0}^{9} e^{u} d u

Nutze das gemeinsame Integral :

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

= 6 \cdot \frac{1}{2} [e^{u}]_{0}^{9}

Vereinfache

6 \cdot \frac{1}{2} [e^{u}]_{0}^{9} : 3 [e^{u}]_{0}^{9}

= 3 [e^{u}]_{0}^{9}

Berechne die Grenzen:

e^{9} - 1

= 3 (e^{9} - 1)

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