integral from 4 to 8 of (4-x)(x-8)

Lösung

\int_{4}^{8} (4 - x) (x - 8) d x

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

\int_{4}^{8} (4 - x) (x - 8) d x

Multipliziere aus

(4 - x) (x - 8) : 12 x - x^{2} - 32

= \int_{4}^{8} 12 x - x^{2} - 32 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_{4}^{8} 12 x d x - \int_{4}^{8} x^{2} d x - \int_{4}^{8} 32 d x

\int_{4}^{8} 12 x d x = 288

\int_{4}^{8} x^{2} d x = \frac{448}{3}

\int_{4}^{8} 32 d x = 128

= 288 - \frac{448}{3} - 128

Vereinfache

288 - \frac{448}{3} - 128 : \frac{32}{3}

= \frac{32}{3}

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