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

Lösung

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

- \frac{π}{3}

Dezimale

- 1.04719 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{3}^{0} \frac{1}{u ^{2} + 1} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{3} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= - [arctan (u)]_{0}^{3}

Berechne die Grenzen:

\frac{π}{3}

= - \frac{π}{3}

\int_{- 1}^{1} t^{2} d t

\int_{0}^{1} a x + b x^{2} d x

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

\int_{0}^{4} x^{2} e^{x^{3}} d x

\int_{0}^{\infty} 5 x e^{- 3 x} d x