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Beliebt Rechnen >

integral from 1 to 10 of (sqrt(x^2-1))/x

Lösung

\int_{1}^{10} \frac{x ^{2} - 1}{x} d x

Lösung

- arctan (311) + 311

+1

Dezimale

8.47924 \dots

Schritte zur Lösung

\int_{1}^{10} \frac{x ^{2} - 1}{x} d x

Wende U-Substitution an

= \int_{0}^{311} \frac{u ^{2}}{u ^{2} + 1} d u

\frac{u ^{2}}{u ^{2} + 1} = - \frac{1}{u ^{2} + 1} + 1

= \int_{0}^{311} - \frac{1}{u ^{2} + 1} + 1 d u

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}^{311} \frac{1}{u ^{2} + 1} d u + \int_{0}^{311} 1 d u

\int_{0}^{311} \frac{1}{u ^{2} + 1} d u = arctan (311)

\int_{0}^{311} 1 d u = 311

= - arctan (311) + 311

Graph

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