integral from-2 to 4 of (x^2-2x-8)

Lösung

\int_{- 2}^{4} (x^{2} - 2 x - 8) d x

- 36

Schritte zur Lösung

\int_{- 2}^{4} x^{2} - 2 x - 8 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_{- 2}^{4} x^{2} d x - \int_{- 2}^{4} 2 x d x - \int_{- 2}^{4} 8 d x

\int_{- 2}^{4} x^{2} d x = 24

\int_{- 2}^{4} 2 x d x = 12

\int_{- 2}^{4} 8 d x = 48

= 24 - 12 - 48

Vereinfache

= - 36