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

Lösung

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

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 4 x d x = 10

\int_{2}^{3} 4 d x = 4

= \frac{19}{3} - 10 + 4

Vereinfache

\frac{19}{3} - 10 + 4 : \frac{1}{3}

= \frac{1}{3}

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