integral from-1 to 1 of (-x^2-2x+8)

Lösung

\int_{- 1}^{1} (- x^{2} - 2 x + 8) d x

\frac{46}{3}

Dezimale

15.33333 \dots

Schritte zur Lösung

\int_{- 1}^{1} - 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_{- 1}^{1} x^{2} d x - \int_{- 1}^{1} 2 x d x + \int_{- 1}^{1} 8 d x

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

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

\int_{- 1}^{1} 8 d x = 16

= - \frac{2}{3} - 0 + 16

Vereinfache

- \frac{2}{3} - 0 + 16 : \frac{46}{3}

= \frac{46}{3}

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