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Beliebt Rechnen >

integral from 1 to 3 of 2\sqrt[4]{x^3}

Lösung

\int_{1}^{3} 2 4 x^{3} d x

Lösung

\frac{2 ( 12 \cdot 3 ^{\frac{3}{4}} - 4 )}{7}

+1

Dezimale

6.67259 \dots

Schritte zur Lösung

\int_{1}^{3} 2 4 x^{3} d x

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{3} 4 x^{3} d x

4 x^{3} = x^{\frac{3}{4}},

angenommen

x \geq 0

= 2 \cdot \int_{1}^{3} x^{\frac{3}{4}} d x

Wende die Potenzregel an

= 2 [\frac{4}{7} x^{\frac{7}{4}}]_{1}^{3}

Berechne die Grenzen:

\frac{12 \cdot 3 ^{\frac{3}{4}}}{7} - \frac{4}{7}

= 2 (\frac{12 \cdot 3 ^{\frac{3}{4}}}{7} - \frac{4}{7})

Vereinfache

= \frac{2 ( 12 \cdot 3 ^{\frac{3}{4}} - 4 )}{7}

Graph

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