integral from-2 to 5 of \sqrt[3]{(3t+8)}

Lösung

\int_{- 2}^{5} 3 (3 t + 8) d t

\frac{23 3 23 \cdot 2 ^{\frac{2}{3}} - 4}{4 \cdot 2 ^{\frac{2}{3}}}

Dezimale

15.72227 \dots

Schritte zur Lösung

\int_{- 2}^{5} 3 3 t + 8 d t

Wende U-Substitution an

= \int_{2}^{23} \frac{3 u}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{2}^{23} 3 u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{3}{4} u^{\frac{4}{3}}]_{2}^{23}

Berechne die Grenzen:

\frac{69 3 23}{4} - \frac{3}{2 ^{\frac{2}{3}}}

= \frac{1}{3} (\frac{69 3 23}{4} - \frac{3}{2 ^{\frac{2}{3}}})

Vereinfache

= \frac{23 3 23 \cdot 2 ^{\frac{2}{3}} - 4}{4 \cdot 2 ^{\frac{2}{3}}}

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