integral from 0 to 1 of 9x^2e^{x^3}

Lösung

\int_{0}^{1} 9 x^{2} e^{x^{3}} d x

3 (e - 1)

Dezimale

5.15484 \dots

Schritte zur Lösung

\int_{0}^{1} 9 x^{2} e^{x^{3}} d x

Entferne die Konstante:

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

= 9 \cdot \int_{0}^{1} x^{2} e^{x^{3}} d x

Wende U-Substitution an

= 9 \cdot \int_{0}^{1} \frac{e ^{u}}{3} d u

Entferne die Konstante:

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

= 9 \cdot \frac{1}{3} \cdot \int_{0}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= 9 \cdot \frac{1}{3} [e^{u}]_{0}^{1}

Vereinfache

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

= 3 [e^{u}]_{0}^{1}

Berechne die Grenzen:

e - 1

= 3 (e - 1)

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