integral from 0 to 2 of 9x^2sqrt(1+x^3)

Lösung

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

52

Schritte zur Lösung

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

Wende U-Substitution an

= 9 \cdot \int_{1}^{9} \frac{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_{1}^{9} u d u

Wende die Potenzregel an

= 9 \cdot \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

Vereinfache

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

= 3 [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

Berechne die Grenzen:

\frac{52}{3}

= 3 \cdot \frac{52}{3}

Vereinfache

= 52

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