integral from 1 to 6 of (sqrt(x^2-1))/x

Lösung

\int_{1}^{6} \frac{x ^{2} - 1}{x} d x

- arctan (35) + 35

Dezimale

4.51273 \dots

Schritte zur Lösung

\int_{1}^{6} \frac{x ^{2} - 1}{x} d x

Wende U-Substitution an

= \int_{0}^{35} \frac{u ^{2}}{u ^{2} + 1} d u

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

= \int_{0}^{35} - \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}^{35} \frac{1}{u ^{2} + 1} d u + \int_{0}^{35} 1 d u

\int_{0}^{35} \frac{1}{u ^{2} + 1} d u = arctan (35)

\int_{0}^{35} 1 d u = 35

= - arctan (35) + 35

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 x - 2, y (0) = 0, y (π) = π

\int 3 x^{3} cos (x^{2}) d x

\int \frac{( 5 x + 3 )}{( x ^{3} - 2 x ^{2} - 3 x )} d x

t an g e n t x^{2} + y^{2} = 169, (- 5, 12)

l a pl a ce t r an s f or m 1 - 2 t