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

Lösung

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

\frac{27}{4}

Dezimale

6.75

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{- b} = \frac{1}{a ^{b}}

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

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

\int_{1}^{8} \frac{1}{x ^{\frac{1}{3}}} d x = \frac{9}{2}

= \frac{45}{4} - \frac{9}{2}

Vereinfache

\frac{45}{4} - \frac{9}{2} : \frac{27}{4}

= \frac{27}{4}

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