integral from 0 to 1 of (sqrt(2x)-x/2)

Lösung

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

- \frac{2}{3} + 2 - \frac{1}{4}

Dezimale

0.69280 \dots

Schritte zur Lösung

\int_{0}^{1} 2 x - \frac{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} 2 x d x - \int_{0}^{1} \frac{x}{2} d x

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

\int_{0}^{1} \frac{x}{2} d x = \frac{1}{4}

= - \frac{2}{3} + 2 - \frac{1}{4}

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