integral from 0 to 4 of x(1+x/2)

Lösung

\int_{0}^{4} x (1 + \frac{x}{2}) d x

\frac{56}{3}

Dezimale

18.66666 \dots

Schritte zur Lösung

\int_{0}^{4} x (1 + \frac{x}{2}) d x

Multipliziere aus

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

= \int_{0}^{4} x + \frac{x ^{2}}{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}^{4} x d x + \int_{0}^{4} \frac{x ^{2}}{2} d x

\int_{0}^{4} x d x = 8

\int_{0}^{4} \frac{x ^{2}}{2} d x = \frac{32}{3}

= 8 + \frac{32}{3}

Vereinfache

8 + \frac{32}{3} : \frac{56}{3}

= \frac{56}{3}

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