integral from-2 to 2 of (1-(x^2)/4)^2

Lösung

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

\frac{32}{15}

Dezimale

2.13333 \dots

Schritte zur Lösung

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

Multipliziere aus

(1 - \frac{x ^{2}}{4})^{2} : 1 - \frac{x ^{2}}{2} + \frac{x ^{4}}{16}

= \int_{- 2}^{2} 1 - \frac{x ^{2}}{2} + \frac{x ^{4}}{16} 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} \frac{x ^{2}}{2} d x + \int_{- 2}^{2} \frac{x ^{4}}{16} d x

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

\int_{- 2}^{2} \frac{x ^{2}}{2} d x = \frac{8}{3}

\int_{- 2}^{2} \frac{x ^{4}}{16} d x = \frac{4}{5}

= 4 - \frac{8}{3} + \frac{4}{5}

Vereinfache

4 - \frac{8}{3} + \frac{4}{5} : \frac{32}{15}

= \frac{32}{15}

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