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

Lösung

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

- \frac{4}{3}

Dezimale

- 1.33333 \dots

Schritte zur Lösung

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

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

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

= 4 - \frac{16}{3}

Vereinfache

4 - \frac{16}{3} : - \frac{4}{3}

= - \frac{4}{3}

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