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

Lösung

\int_{0}^{4} π (4 x)^{2} d x

\frac{1024 π}{3}

Dezimale

1072.33029 \dots

Schritte zur Lösung

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

Vereinfache

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

= π \cdot \int_{0}^{4} 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}^{4} x^{2} d x

Wende die Potenzregel an

= π 16 [\frac{x ^{3}}{3}]_{0}^{4}

Berechne die Grenzen:

\frac{64}{3}

= π 16 \cdot \frac{64}{3}

Vereinfache

= \frac{1024 π}{3}

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

\int_{0}^{1} \frac{32}{9} (x y)^{\frac{1}{3}} d y

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