integral from-2 to-1 of-x^2-2x-x-2

Lösung

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

\frac{1}{6}

Dezimale

0.16666 \dots

Schritte zur Lösung

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

Vereinfache

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

\int_{- 2}^{- 1} x^{2} d x = \frac{7}{3}

\int_{- 2}^{- 1} 3 x d x = - \frac{9}{2}

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

= - \frac{7}{3} - (- \frac{9}{2}) - 2

Vereinfache

- \frac{7}{3} - (- \frac{9}{2}) - 2 : \frac{1}{6}

= \frac{1}{6}

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