integral from 8 to 27 of (\sqrt[3]{x}-1/(\sqrt[3]{x)})

Lösung

\int_{8}^{27} (3 x - \frac{1}{3 x}) d x

\frac{165}{4}

Dezimale

41.25

Schritte zur Lösung

\int_{8}^{27} 3 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_{8}^{27} 3 x d x - \int_{8}^{27} \frac{1}{3 x} d x

\int_{8}^{27} 3 x d x = \frac{195}{4}

\int_{8}^{27} \frac{1}{3 x} d x = \frac{15}{2}

= \frac{195}{4} - \frac{15}{2}

Vereinfache

\frac{195}{4} - \frac{15}{2} : \frac{165}{4}

= \frac{165}{4}

\int_{- 2}^{- 1} \frac{1}{( x - 1 ) ^{2}} d x

\int_{1}^{2} \frac{4}{2} d x

\int_{0}^{1} x x + 3 d x

\int_{0}^{4} \frac{3}{16} x d x

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