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Beliebt Rechnen >

integral from 0 to 1 of (1+x)^2

Lösung

\int_{0}^{1} (1 + x)^{2} d x

Lösung

\frac{7}{3}

+1

Dezimale

2.33333 \dots

Schritte zur Lösung

\int_{0}^{1} (1 + x)^{2} d x

Multipliziere aus

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

= \int_{0}^{1} 1 + 2 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}^{1} 1 d x + \int_{0}^{1} 2 x d x + \int_{0}^{1} x^{2} d x

\int_{0}^{1} 1 d x = 1

\int_{0}^{1} 2 x d x = 1

\int_{0}^{1} x^{2} d x = \frac{1}{3}

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

Vereinfache

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

= \frac{7}{3}

Graph

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