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

Lösung

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

- \frac{1}{12}

Dezimale

- 0.08333 \dots

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{1} x - x 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

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

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

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

= \frac{1}{2} (\frac{1}{2} - \frac{2}{3})

Vereinfache

\frac{1}{2} (\frac{1}{2} - \frac{2}{3}) : - \frac{1}{12}

= - \frac{1}{12}

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