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Beliebt Rechnen >

integral from 1 to 2 of (x-1)^2

Lösung

\int_{1}^{2} (x - 1)^{2} d x

Lösung

\frac{1}{3}

+1

Dezimale

0.33333 \dots

Schritte zur Lösung

\int_{1}^{2} (x - 1)^{2} d x

Multipliziere aus

(x - 1)^{2} : x^{2} - 2 x + 1

= \int_{1}^{2} x^{2} - 2 x + 1 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}^{2} x^{2} d x - \int_{1}^{2} 2 x d x + \int_{1}^{2} 1 d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} 2 x d x = 3

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

= \frac{7}{3} - 3 + 1

Vereinfache

\frac{7}{3} - 3 + 1 : \frac{1}{3}

= \frac{1}{3}

Graph

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