integral from-1 to 2 of (2x^2-2x-4)

Lösung

\int_{- 1}^{2} (2 x^{2} - 2 x - 4) d x

- 9

Schritte zur Lösung

\int_{- 1}^{2} 2 x^{2} - 2 x - 4 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_{- 1}^{2} 2 x^{2} d x - \int_{- 1}^{2} 2 x d x - \int_{- 1}^{2} 4 d x

\int_{- 1}^{2} 2 x^{2} d x = 6

\int_{- 1}^{2} 2 x d x = 3

\int_{- 1}^{2} 4 d x = 12

= 6 - 3 - 12

Vereinfache

= - 9

\int_{0}^{2} \frac{12}{x ^{2} - 4} d x

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