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

Lösung

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

\frac{1}{6}

Dezimale

0.16666 \dots

Schritte zur Lösung

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

Vereinfache

= \int_{1}^{2} x - 1 - x + 1 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_{1}^{2} x - 1 d x - \int_{1}^{2} x d x + \int_{1}^{2} 1 d x

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

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

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

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

Vereinfache

\frac{2}{3} - \frac{3}{2} + 1 : \frac{1}{6}

= \frac{1}{6}

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

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