integral from 0 to 24 of x^2(1/288 x)

Lösung

\int_{0}^{24} x^{2} (\frac{1}{288} x) d x

288

Schritte zur Lösung

\int_{0}^{24} x^{2} \frac{1}{288} x d x

Entferne die Konstante:

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

= \frac{1}{288} \cdot \int_{0}^{24} x^{2} x d x

Vereinfache

x^{2} x : x^{3}

= \frac{1}{288} \cdot \int_{0}^{24} x^{3} d x

Wende die Potenzregel an

= \frac{1}{288} [\frac{x ^{4}}{4}]_{0}^{24}

Berechne die Grenzen:

82944

= \frac{1}{288} \cdot 82944

Vereinfache

= 288

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