integral from-1 to 8 of (x^{1/3}-x)

Lösung

\int_{- 1}^{8} (x^{\frac{1}{3}} - x) d x

- \frac{81}{4}

Dezimale

- 20.25

Schritte zur Lösung

\int_{- 1}^{8} x^{\frac{1}{3}} - x 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

= \int_{- 1}^{8} x^{\frac{1}{3}} d x - \int_{- 1}^{8} x d x

\int_{- 1}^{8} x^{\frac{1}{3}} d x = \frac{45}{4}

\int_{- 1}^{8} x d x = \frac{63}{2}

= \frac{45}{4} - \frac{63}{2}

Vereinfache

\frac{45}{4} - \frac{63}{2} : - \frac{81}{4}

= - \frac{81}{4}

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