integral from 0 to 1 of 2pi(x+10)x^2

Lösung

\int_{0}^{1} 2 π (x + 10) x^{2} d x

\frac{43 π}{6}

Dezimale

22.51474 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π (x + 10) 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}^{1} (x + 10) x^{2} d x

Multipliziere aus

(x + 10) x^{2} : x^{3} + 10 x^{2}

= 2 π \cdot \int_{0}^{1} x^{3} + 10 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

= 2 π (\int_{0}^{1} x^{3} d x + \int_{0}^{1} 10 x^{2} d x)

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

\int_{0}^{1} 10 x^{2} d x = \frac{10}{3}

= 2 π (\frac{1}{4} + \frac{10}{3})

Vereinfache

2 π (\frac{1}{4} + \frac{10}{3}) : \frac{43 π}{6}

= \frac{43 π}{6}

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