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Beliebt Rechnen >

integral from 0 to 1 of 2pi(x^5-x^6)

Lösung

\int_{0}^{1} 2 π (x^{5} - x^{6}) d x

Lösung

\frac{π}{21}

+1

Dezimale

0.14959 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π (x^{5} - x^{6}) 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^{5} - x^{6} 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^{5} d x - \int_{0}^{1} x^{6} d x)

\int_{0}^{1} x^{5} d x = \frac{1}{6}

\int_{0}^{1} x^{6} d x = \frac{1}{7}

= 2 π (\frac{1}{6} - \frac{1}{7})

Vereinfache

2 π (\frac{1}{6} - \frac{1}{7}) : \frac{π}{21}

= \frac{π}{21}

Graph

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