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Beliebt Rechnen >

integral from 0 to 6 of pi/8 (6-x)^2

Lösung

\int_{0}^{6} \frac{π}{8} (6 - x)^{2} d x

Lösung

9 π

+1

Dezimale

28.27433 \dots

Schritte zur Lösung

\int_{0}^{6} \frac{π}{8} (6 - x)^{2} d x

Entferne die Konstante:

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

= \frac{π}{8} \cdot \int_{0}^{6} (6 - x)^{2} d x

Multipliziere aus

(6 - x)^{2} : 36 - 12 x + x^{2}

= \frac{π}{8} \cdot \int_{0}^{6} 36 - 12 x + 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

= \frac{π}{8} (\int_{0}^{6} 36 d x - \int_{0}^{6} 12 x d x + \int_{0}^{6} x^{2} d x)

\int_{0}^{6} 36 d x = 216

\int_{0}^{6} 12 x d x = 216

\int_{0}^{6} x^{2} d x = 72

= \frac{π}{8} (216 - 216 + 72)

Vereinfache

\frac{π}{8} (216 - 216 + 72) : 9 π

= 9 π

Graph

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