integral from 0 to 5 of pix^2

Lösung

\int_{0}^{5} π x^{2} d x

\frac{125 π}{3}

Dezimale

130.89969 \dots

Schritte zur Lösung

\int_{0}^{5} π 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}^{5} x^{2} d x

Wende die Potenzregel an

= π [\frac{x ^{3}}{3}]_{0}^{5}

Berechne die Grenzen:

\frac{125}{3}

= π \frac{125}{3}

Vereinfache

= \frac{125 π}{3}

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