integral from 1 to 7 of (1-x)(x-7)

Lösung

\int_{1}^{7} (1 - x) (x - 7) d x

36

Schritte zur Lösung

\int_{1}^{7} (1 - x) (x - 7) d x

Multipliziere aus

(1 - x) (x - 7) : 8 x - x^{2} - 7

= \int_{1}^{7} 8 x - x^{2} - 7 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}^{7} 8 x d x - \int_{1}^{7} x^{2} d x - \int_{1}^{7} 7 d x

\int_{1}^{7} 8 x d x = 192

\int_{1}^{7} x^{2} d x = 114

\int_{1}^{7} 7 d x = 42

= 192 - 114 - 42

Vereinfache

= 36

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