integral from-1 to 0 of 6x^2(2x^3+4)^2

Lösung

\int_{- 1}^{0} 6 x^{2} (2 x^{3} + 4)^{2} d x

\frac{56}{3}

Dezimale

18.66666 \dots

Schritte zur Lösung

\int_{- 1}^{0} 6 x^{2} (2 x^{3} + 4)^{2} d x

Entferne die Konstante:

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

= 6 \cdot \int_{- 1}^{0} x^{2} (2 x^{3} + 4)^{2} d x

Wende U-Substitution an

= 6 \cdot \int_{2}^{4} \frac{u ^{2}}{6} d u

Entferne die Konstante:

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

= 6 \cdot \frac{1}{6} \cdot \int_{2}^{4} u^{2} d u

Wende die Potenzregel an

= 6 \cdot \frac{1}{6} [\frac{u ^{3}}{3}]_{2}^{4}

Vereinfache

6 \cdot \frac{1}{6} [\frac{u ^{3}}{3}]_{2}^{4} : [\frac{u ^{3}}{3}]_{2}^{4}

= [\frac{u ^{3}}{3}]_{2}^{4}

Berechne die Grenzen:

\frac{56}{3}

= \frac{56}{3}

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