integral from 0 to 1 of pi(x-x^8)

Lösung

\int_{0}^{1} π (x - x^{8}) d x

π \frac{7}{18}

Dezimale

1.22173 \dots

Schritte zur Lösung

\int_{0}^{1} π (x - x^{8}) d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{1} x - x^{8} 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} x d x - \int_{0}^{1} x^{8} d x)

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

\int_{0}^{1} x^{8} d x = \frac{1}{9}

= π (\frac{1}{2} - \frac{1}{9})

Füge

\frac{1}{2} - \frac{1}{9}

zusammen:

\frac{7}{18}

= π \frac{7}{18}

\int_{1}^{\infty} x^{- 4} d x

d er i v a t i v e 6 x^{5} + 4 e^{x}

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