integral of (12-x)^2

Lösung

\int (12 - x)^{2} d x

144 x - 12 x^{2} + \frac{x ^{3}}{3} + C

Schritte zur Lösung

\int (12 - x)^{2} d x

Multipliziere aus

(12 - x)^{2} : 144 - 24 x + x^{2}

= \int 144 - 24 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 144 d x - \int 24 x d x + \int x^{2} d x

\int 144 d x = 144 x

\int 24 x d x = 12 x^{2}

\int x^{2} d x = \frac{x ^{3}}{3}

= 144 x - 12 x^{2} + \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= 144 x - 12 x^{2} + \frac{x ^{3}}{3} + C

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