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

Lösung

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

\frac{160 5}{3}

Dezimale

119.25695 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{80} \frac{u}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{0}^{80} u d u

Wende die Potenzregel an

= \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{80}

Berechne die Grenzen:

\frac{640 5}{3}

= \frac{1}{4} \cdot \frac{640 5}{3}

Vereinfache

= \frac{160 5}{3}

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