integral from 1 to 7 of (sqrt(x^2-1))/x

Lösung

\int_{1}^{7} \frac{x ^{2} - 1}{x} d x

- arctan (43) + 43

Dezimale

5.50075 \dots

Schritte zur Lösung

\int_{1}^{7} \frac{x ^{2} - 1}{x} d x

Wende U-Substitution an

= \int_{0}^{43} \frac{u ^{2}}{u ^{2} + 1} d u

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

= \int_{0}^{43} - \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}^{43} \frac{1}{u ^{2} + 1} d u + \int_{0}^{43} 1 d u

\int_{0}^{43} \frac{1}{u ^{2} + 1} d u = arctan (43)

\int_{0}^{43} 1 d u = 43

= - arctan (43) + 43

\frac{d}{d t} (t - 1)

d er i v a t i v e f (x) = 645120

\int_{- \infty}^{0} z e^{4 z} d z

t an g e n t f (x) = (x - 5)^{5}, at x = 6

d er i v a t i v e x + \frac{1}{x ^{2}}