integral from 0 to 5 of (x-4)^2

Lösung

\int_{0}^{5} (x - 4)^{2} d x

\frac{65}{3}

Dezimale

21.66666 \dots

Schritte zur Lösung

\int_{0}^{5} (x - 4)^{2} d x

Multipliziere aus

(x - 4)^{2} : x^{2} - 8 x + 16

= \int_{0}^{5} x^{2} - 8 x + 16 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}^{5} x^{2} d x - \int_{0}^{5} 8 x d x + \int_{0}^{5} 16 d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} 8 x d x = 100

\int_{0}^{5} 16 d x = 80

= \frac{125}{3} - 100 + 80

Vereinfache

\frac{125}{3} - 100 + 80 : \frac{65}{3}

= \frac{65}{3}

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