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

Lösung

\int_{0}^{3} 2 π x (x^{2}) d x

\frac{81 π}{2}

Dezimale

127.23450 \dots

Schritte zur Lösung

\int_{0}^{3} 2 π x x^{2} d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{3} x x^{2} d x

Vereinfache

x x^{2} : x^{3}

= 2 π \cdot \int_{0}^{3} x^{3} d x

Wende die Potenzregel an

= 2 π [\frac{x ^{4}}{4}]_{0}^{3}

Berechne die Grenzen:

\frac{81}{4}

= 2 π \frac{81}{4}

Vereinfache

= \frac{81 π}{2}

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