integral from 1 to 3 of \sqrt[3]{x^2}

Lösung

\int_{1}^{3} 3 x^{2} d x

\frac{9 \cdot 3 ^{\frac{2}{3}} - 3}{5}

Dezimale

3.14415 \dots

Schritte zur Lösung

\int_{1}^{3} 3 x^{2} d x

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

angenommen

x \geq 0

= \int_{1}^{3} x^{\frac{2}{3}} d x

Wende die Potenzregel an

= [\frac{3}{5} x^{\frac{5}{3}}]_{1}^{3}

Berechne die Grenzen:

\frac{9 \cdot 3 ^{\frac{2}{3}}}{5} - \frac{3}{5}

= \frac{9 \cdot 3 ^{\frac{2}{3}}}{5} - \frac{3}{5}

Vereinfache

= \frac{9 \cdot 3 ^{\frac{2}{3}} - 3}{5}

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