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

Lösung

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

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

\int_{0}^{1} 2 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

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

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

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

= 1 - \frac{2}{3}

Vereinfache

1 - \frac{2}{3} : \frac{1}{3}

= \frac{1}{3}

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