integral from 0 to 2 of (3x)^2

Lösung

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

24

Schritte zur Lösung

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

Vereinfache

(3 x)^{2} : 9 x^{2}

= \int_{0}^{2} 9 x^{2} d x

Entferne die Konstante:

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

= 9 \cdot \int_{0}^{2} x^{2} d x

Wende die Potenzregel an

= 9 [\frac{x ^{3}}{3}]_{0}^{2}

Berechne die Grenzen:

\frac{8}{3}

= 9 \cdot \frac{8}{3}

Vereinfache

= 24

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