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Beliebt Rechnen >

integral from 0 to 1 of 4pi(x^2-x^{10})

Lösung

\int_{0}^{1} 4 π (x^{2} - x^{10}) d x

Lösung

\frac{32 π}{33}

+1

Dezimale

3.04639 \dots

Schritte zur Lösung

\int_{0}^{1} 4 π (x^{2} - x^{10}) d x

Entferne die Konstante:

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

= 4 π \cdot \int_{0}^{1} x^{2} - x^{10} 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

= 4 π (\int_{0}^{1} x^{2} d x - \int_{0}^{1} x^{10} d x)

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

\int_{0}^{1} x^{10} d x = \frac{1}{11}

= 4 π (\frac{1}{3} - \frac{1}{11})

Vereinfache

4 π (\frac{1}{3} - \frac{1}{11}) : \frac{32 π}{33}

= \frac{32 π}{33}

Graph

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