integral from-2 to 2 of (4-y^2)-(y^2-4)

Lösung

\int_{- 2}^{2} (4 - y^{2}) - (y^{2} - 4) d y

\frac{64}{3}

Dezimale

21.33333 \dots

Schritte zur Lösung

\int_{- 2}^{2} 4 - y^{2} - (y^{2} - 4) d y

Vereinfache

= \int_{- 2}^{2} - 2 y^{2} + 8 d y

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} 2 y^{2} d y + \int_{- 2}^{2} 8 d y

\int_{- 2}^{2} 2 y^{2} d y = \frac{32}{3}

\int_{- 2}^{2} 8 d y = 32

= - \frac{32}{3} + 32

Vereinfache

- \frac{32}{3} + 32 : \frac{64}{3}

= \frac{64}{3}

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