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Beliebt Rechnen >

integral from-1 to 2 of 3xsqrt(4x^2-2)

Lösung

\int_{- 1}^{2} 3 x 4 x^{2} - 2 d x

Lösung

\frac{7 14 - 2}{2}

+1

Dezimale

12.38869 \dots

Schritte zur Lösung

\int_{- 1}^{2} 3 x 4 x^{2} - 2 d x

Entferne die Konstante:

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

= 3 \cdot \int_{- 1}^{2} x 4 x^{2} - 2 d x

Wende U-Substitution an

= 3 \cdot \int_{2}^{14} \frac{u}{8} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{8} \cdot \int_{2}^{14} u d u

Wende die Potenzregel an

= 3 \cdot \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{14}

Vereinfache

3 \cdot \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{14} : \frac{3}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{14}

= \frac{3}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{14}

Berechne die Grenzen:

\frac{28 14 - 4 2}{3}

= \frac{3}{8} \cdot \frac{28 14 - 4 2}{3}

Vereinfache

= \frac{7 14 - 2}{2}

Graph

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