integral from-2 to 0 of (u^5-u^3+u^2)

Lösung

\int_{- 2}^{0} (u^{5} - u^{3} + u^{2}) d u

- 4

Schritte zur Lösung

\int_{- 2}^{0} u^{5} - u^{3} + u^{2} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 2}^{0} u^{5} d u - \int_{- 2}^{0} u^{3} d u + \int_{- 2}^{0} u^{2} d u

\int_{- 2}^{0} u^{5} d u = - \frac{32}{3}

\int_{- 2}^{0} u^{3} d u = - 4

\int_{- 2}^{0} u^{2} d u = \frac{8}{3}

= - \frac{32}{3} - (- 4) + \frac{8}{3}

Vereinfache

- \frac{32}{3} - (- 4) + \frac{8}{3} : - 4

= - 4

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