integral from 2 to 4 of (x-2)^2

Lösung

\int_{2}^{4} (x - 2)^{2} d x

\frac{8}{3}

Dezimale

2.66666 \dots

Schritte zur Lösung

\int_{2}^{4} (x - 2)^{2} d x

Multipliziere aus

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

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

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 4 x d x = 24

\int_{2}^{4} 4 d x = 8

= \frac{56}{3} - 24 + 8

Vereinfache

\frac{56}{3} - 24 + 8 : \frac{8}{3}

= \frac{8}{3}

\int_{- 2}^{x} (16 x^{2} - 15 x) d x

\int_{1}^{e} \frac{1}{2 x} d x

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