integral from 0 to 1 of sqrt(x)(x^2-1)

Lösung

\int_{0}^{1} x (x^{2} - 1) d x

- \frac{8}{21}

Dezimale

- 0.38095 \dots

Schritte zur Lösung

\int_{0}^{1} x (x^{2} - 1) d x

Multipliziere aus

x (x^{2} - 1) : x^{\frac{5}{2}} - x

= \int_{0}^{1} x^{\frac{5}{2}} - 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{5}{2}} d x - \int_{0}^{1} x d x

\int_{0}^{1} x^{\frac{5}{2}} d x = \frac{2}{7}

\int_{0}^{1} x d x = \frac{2}{3}

= \frac{2}{7} - \frac{2}{3}

Vereinfache

\frac{2}{7} - \frac{2}{3} : - \frac{8}{21}

= - \frac{8}{21}

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