integral from 3 to 8 of (3-x)(x-8)

Lösung

\int_{3}^{8} (3 - x) (x - 8) d x

\frac{125}{6}

Dezimale

20.83333 \dots

Schritte zur Lösung

\int_{3}^{8} (3 - x) (x - 8) d x

Multipliziere aus

(3 - x) (x - 8) : 11 x - x^{2} - 24

= \int_{3}^{8} 11 x - x^{2} - 24 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_{3}^{8} 11 x d x - \int_{3}^{8} x^{2} d x - \int_{3}^{8} 24 d x

\int_{3}^{8} 11 x d x = \frac{605}{2}

\int_{3}^{8} x^{2} d x = \frac{485}{3}

\int_{3}^{8} 24 d x = 120

= \frac{605}{2} - \frac{485}{3} - 120

Vereinfache

\frac{605}{2} - \frac{485}{3} - 120 : \frac{125}{6}

= \frac{125}{6}