integral from 0 to 3 of (2-x)^2

Lösung

\int_{0}^{3} (2 - x)^{2} d x

3

Schritte zur Lösung

\int_{0}^{3} (2 - x)^{2} d x

Multipliziere aus

(2 - x)^{2} : 4 - 4 x + x^{2}

= \int_{0}^{3} 4 - 4 x + x^{2} 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_{0}^{3} 4 d x - \int_{0}^{3} 4 x d x + \int_{0}^{3} x^{2} d x

\int_{0}^{3} 4 d x = 12

\int_{0}^{3} 4 x d x = 18

\int_{0}^{3} x^{2} d x = 9

= 12 - 18 + 9

Vereinfache

= 3

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