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

Lösung

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

\frac{8}{3}

Dezimale

2.66666 \dots

Schritte zur Lösung

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

Vereinfache

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

\int_{- 1}^{1} 2 x^{2} d x = \frac{4}{3}

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

= - \frac{4}{3} + 4

Vereinfache

- \frac{4}{3} + 4 : \frac{8}{3}

= \frac{8}{3}

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