integral from 1 to 9 of (1-x)(x-9)

Lösung

\int_{1}^{9} (1 - x) (x - 9) d x

\frac{256}{3}

Dezimale

85.33333 \dots

Schritte zur Lösung

\int_{1}^{9} (1 - x) (x - 9) d x

Multipliziere aus

(1 - x) (x - 9) : 10 x - x^{2} - 9

= \int_{1}^{9} 10 x - x^{2} - 9 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_{1}^{9} 10 x d x - \int_{1}^{9} x^{2} d x - \int_{1}^{9} 9 d x

\int_{1}^{9} 10 x d x = 400

\int_{1}^{9} x^{2} d x = \frac{728}{3}

\int_{1}^{9} 9 d x = 72

= 400 - \frac{728}{3} - 72

Vereinfache

400 - \frac{728}{3} - 72 : \frac{256}{3}

= \frac{256}{3}