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Beliebt Rechnen >

integral from 0 to 1 of pi(5x^2)^2

Lösung

\int_{0}^{1} π (5 x^{2})^{2} d x

Lösung

5 π

+1

Dezimale

15.70796 \dots

Schritte zur Lösung

\int_{0}^{1} π (5 x^{2})^{2} d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{1} (5 x^{2})^{2} d x

Vereinfache

(5 x^{2})^{2} : 25 x^{4}

= π \cdot \int_{0}^{1} 25 x^{4} d x

Entferne die Konstante:

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

= π 25 \cdot \int_{0}^{1} x^{4} d x

Wende die Potenzregel an

= π 25 [\frac{x ^{5}}{5}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{5}

= π 25 \cdot \frac{1}{5}

Vereinfache

= 5 π

Graph

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