integral from-3 to 0 of (4x^{1/3})

Lösung

\int_{- 3}^{0} (4 x^{\frac{1}{3}}) d x

9 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}}

Schritte zur Lösung

\int_{- 3}^{0} 4 x^{\frac{1}{3}} d x

Entferne die Konstante:

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

= 4 \cdot \int_{- 3}^{0} x^{\frac{1}{3}} d x

Wende die Potenzregel an

= 4 [\frac{3}{4} x^{\frac{4}{3}}]_{- 3}^{0}

Berechne die Grenzen:

\frac{9 ( - 1 ) ^{\frac{1}{3}} \cdot 3 ^{\frac{1}{3}}}{4}

= 4 \cdot \frac{9 ( - 1 ) ^{\frac{1}{3}} \cdot 3 ^{\frac{1}{3}}}{4}

Vereinfache

= 9 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}}

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