integral from 1 to 8 of (sqrt(x^2-1))/x

Lösung

\int_{1}^{8} \frac{x ^{2} - 1}{x} d x

- arctan (37) + 37

Dezimale

6.49178 \dots

Schritte zur Lösung

\int_{1}^{8} \frac{x ^{2} - 1}{x} d x

Wende U-Substitution an

= \int_{0}^{37} \frac{u ^{2}}{u ^{2} + 1} d u

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

= \int_{0}^{37} - \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}^{37} \frac{1}{u ^{2} + 1} d u + \int_{0}^{37} 1 d u

\int_{0}^{37} \frac{1}{u ^{2} + 1} d u = arctan (37)

\int_{0}^{37} 1 d u = 37

= - arctan (37) + 37

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