integral from 3 to 9 of (3-x)(x-9)

Lösung

\int_{3}^{9} (3 - x) (x - 9) d x

36

Schritte zur Lösung

\int_{3}^{9} (3 - x) (x - 9) d x

Multipliziere aus

(3 - x) (x - 9) : 12 x - x^{2} - 27

= \int_{3}^{9} 12 x - x^{2} - 27 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}^{9} 12 x d x - \int_{3}^{9} x^{2} d x - \int_{3}^{9} 27 d x

\int_{3}^{9} 12 x d x = 432

\int_{3}^{9} x^{2} d x = 234

\int_{3}^{9} 27 d x = 162

= 432 - 234 - 162

Vereinfache

= 36

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