integral from 0 to 1 of x^{1/5}-x

Lösung

\int_{0}^{1} x^{\frac{1}{5}} - x d x

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

\int_{0}^{1} x^{\frac{1}{5}} - 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_{0}^{1} x^{\frac{1}{5}} d x - \int_{0}^{1} x d x

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

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

= \frac{5}{6} - \frac{1}{2}

Vereinfache

\frac{5}{6} - \frac{1}{2} : \frac{1}{3}

= \frac{1}{3}

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