integral from 0 to 5 of 7*\sqrt[3]{x^2}

Lösung

\int_{0}^{5} 7 \cdot 3 x^{2} d x

21 \cdot 5^{\frac{2}{3}}

Dezimale

61.40437 \dots

Schritte zur Lösung

\int_{0}^{5} 7 3 x^{2} d x

Entferne die Konstante:

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

= 7 \cdot \int_{0}^{5} 3 x^{2} d x

3 x^{2} = x^{\frac{2}{3}},

angenommen

x \geq 0

= 7 \cdot \int_{0}^{5} x^{\frac{2}{3}} d x

Wende die Potenzregel an

= 7 [\frac{3}{5} x^{\frac{5}{3}}]_{0}^{5}

Berechne die Grenzen:

3 \cdot 5^{\frac{2}{3}}

= 7 \cdot 3 \cdot 5^{\frac{2}{3}}

Vereinfache

= 21 \cdot 5^{\frac{2}{3}}

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