integral from 0 to 1 of \sqrt[3]{(1+7x)}

Lösung

\int_{0}^{1} 3 (1 + 7 x) d x

\frac{45}{28}

Dezimale

1.60714 \dots

Schritte zur Lösung

\int_{0}^{1} 3 1 + 7 x d x

Wende U-Substitution an

= \int_{1}^{8} \frac{3 u}{7} d u

Entferne die Konstante:

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

= \frac{1}{7} \cdot \int_{1}^{8} 3 u d u

Wende die Potenzregel an

= \frac{1}{7} [\frac{3}{4} u^{\frac{4}{3}}]_{1}^{8}

Berechne die Grenzen:

\frac{45}{4}

= \frac{1}{7} \cdot \frac{45}{4}

Vereinfache

= \frac{45}{28}

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