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

Lösung

\int_{0}^{2} x^{2} - \frac{x ^{2}}{4} d x

2

Schritte zur Lösung

\int_{0}^{2} x^{2} - \frac{x ^{2}}{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_{0}^{2} x^{2} d x - \int_{0}^{2} \frac{x ^{2}}{4} d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

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

= \frac{8}{3} - \frac{2}{3}

Vereinfache

\frac{8}{3} - \frac{2}{3} : 2

= 2

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