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Beliebt Rechnen >

integral from 0 to 4 of pi(16-x^2)

Lösung

\int_{0}^{4} π (16 - x^{2}) d x

Lösung

π \frac{128}{3}

+1

Dezimale

134.04128 \dots

Schritte zur Lösung

\int_{0}^{4} π (16 - 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} 16 - x^{2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{0}^{4} 16 d x - \int_{0}^{4} x^{2} d x)

\int_{0}^{4} 16 d x = 64

\int_{0}^{4} x^{2} d x = \frac{64}{3}

= π (64 - \frac{64}{3})

Füge

64 - \frac{64}{3}

zusammen:

\frac{128}{3}

= π \frac{128}{3}

Graph

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