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

Lösung

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

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

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

Entferne die Extremwerte

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

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

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

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

Vereinfache

- \frac{2}{3} + 2 : \frac{4}{3}

= \frac{4}{3}

\int_{0}^{2} (x - 1) d x

\int_{1}^{2} (4 x^{3} - 3 x^{2} + 2) d x

\int_{2}^{3} \frac{x + 1}{x} d x

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\int_{2}^{8} x^{2} d x