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Beliebt Rechnen >

integral from 0 to 1 of pi(6-3/2 x)^2

Lösung

\int_{0}^{1} π (6 - \frac{3}{2} x)^{2} d x

Lösung

π \frac{111}{4}

+1

Dezimale

87.17919 \dots

Schritte zur Lösung

\int_{0}^{1} π (6 - \frac{3}{2} 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}^{1} (6 - \frac{3}{2} x)^{2} d x

Vereinfache

(6 - \frac{3}{2} x)^{2} : 36 - 18 x + \frac{9}{4} x^{2}

= π \cdot \int_{0}^{1} 36 - 18 x + \frac{9}{4} 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}^{1} 36 d x - \int_{0}^{1} 18 x d x + \int_{0}^{1} \frac{9}{4} x^{2} d x)

\int_{0}^{1} 36 d x = 36

\int_{0}^{1} 18 x d x = 9

\int_{0}^{1} \frac{9}{4} x^{2} d x = \frac{3}{4}

= π (36 - 9 + \frac{3}{4})

Vereinfache

π (36 - 9 + \frac{3}{4}) : π \frac{111}{4}

= π \frac{111}{4}

Graph

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