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

Lösung

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

\frac{512}{15}

Dezimale

34.13333 \dots

Schritte zur Lösung

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

Multipliziere aus

(4 - y^{2})^{2} : 16 - 8 y^{2} + y^{4}

= \int_{- 2}^{2} 16 - 8 y^{2} + y^{4} 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} 16 d y - \int_{- 2}^{2} 8 y^{2} d y + \int_{- 2}^{2} y^{4} d y

\int_{- 2}^{2} 16 d y = 64

\int_{- 2}^{2} 8 y^{2} d y = \frac{128}{3}

\int_{- 2}^{2} y^{4} d y = \frac{64}{5}

= 64 - \frac{128}{3} + \frac{64}{5}

Vereinfache

64 - \frac{128}{3} + \frac{64}{5} : \frac{512}{15}

= \frac{512}{15}

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