integral from 0 to 1 of (3x+2)^4

Lösung

\int_{0}^{1} (3 x + 2)^{4} d x

\frac{1031}{5}

Dezimale

206.2

Schritte zur Lösung

\int_{0}^{1} (3 x + 2)^{4} d x

Wende U-Substitution an

= \int_{2}^{5} \frac{u ^{4}}{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}^{5} u^{4} d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{u ^{5}}{5}]_{2}^{5}

Berechne die Grenzen:

\frac{3093}{5}

= \frac{1}{3} \cdot \frac{3093}{5}

Vereinfache

= \frac{1031}{5}

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