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

Lösung

\int_{0}^{3} π (4 x)^{2} d x

144 π

Dezimale

452.38934 \dots

Schritte zur Lösung

\int_{0}^{3} π (4 x)^{2} d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{3} (4 x)^{2} d x

Vereinfache

(4 x)^{2} : 16 x^{2}

= π \cdot \int_{0}^{3} 16 x^{2} d x

Entferne die Konstante:

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

= π 16 \cdot \int_{0}^{3} x^{2} d x

Wende die Potenzregel an

= π 16 [\frac{x ^{3}}{3}]_{0}^{3}

Berechne die Grenzen:

9

= π 16 \cdot 9

Vereinfache

= 144 π

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