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

Lösung

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

\frac{52}{3}

Dezimale

17.33333 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= 3 \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

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

Wende die Potenzregel an

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

Vereinfache

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

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

Berechne die Grenzen:

\frac{52}{3}

= \frac{52}{3}

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