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

Lösung

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

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

\int_{- 2}^{2} 4 + y^{2} - 2 y^{2} d y

Vereinfache

= \int_{- 2}^{2} 4 - y^{2} 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} 4 d y - \int_{- 2}^{2} y^{2} d y

\int_{- 2}^{2} 4 d y = 16

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

= 16 - \frac{16}{3}

Vereinfache

16 - \frac{16}{3} : \frac{32}{3}

= \frac{32}{3}

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