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Beliebt Rechnen >

integral from 0 to 4 of (16-x^2)^2

Lösung

\int_{0}^{4} (16 - x^{2})^{2} d x

Lösung

\frac{8192}{15}

+1

Dezimale

546.13333 \dots

Schritte zur Lösung

\int_{0}^{4} (16 - x^{2})^{2} d x

Multipliziere aus

(16 - x^{2})^{2} : 256 - 32 x^{2} + x^{4}

= \int_{0}^{4} 256 - 32 x^{2} + x^{4} 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_{0}^{4} 256 d x - \int_{0}^{4} 32 x^{2} d x + \int_{0}^{4} x^{4} d x

\int_{0}^{4} 256 d x = 1024

\int_{0}^{4} 32 x^{2} d x = \frac{2048}{3}

\int_{0}^{4} x^{4} d x = \frac{1024}{5}

= 1024 - \frac{2048}{3} + \frac{1024}{5}

Vereinfache

1024 - \frac{2048}{3} + \frac{1024}{5} : \frac{8192}{15}

= \frac{8192}{15}

Graph

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