integral from-1 to 0 of 1/(sqrt(x^2-2x))

Lösung

\int_{- 1}^{0} \frac{1}{x ^{2} - 2 x} d x

- ln (2 + 3)

Dezimale

- 1.31695 \dots

Schritte zur Lösung

\int_{- 1}^{0} \frac{1}{x ^{2} - 2 x} d x

Vervollständige das Quadrat

x^{2} - 2 x : (x - 1)^{2} - 1

= \int_{- 1}^{0} \frac{1}{( x - 1 ) ^{2} - 1} d x

Wende U-Substitution an

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

Trigonometrische Substitution anwenden

= \int_{\frac{2 π}{3}}^{π} sec (v) d v

Nutze das gemeinsame Integral :

\int sec (v) d v = ln ∣ tan (v) + sec (v) ∣

= [ln ∣ tan (v) + sec (v) ∣]_{\frac{2 π}{3}}^{π}

Berechne die Grenzen:

- ln (2 + 3)

= - ln (2 + 3)

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

\int_{0}^{2 π} s^{2} d s

\int_{5}^{10} 2 x^{- 3} d x

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

\int_{1}^{3} 2 x^{2} - x d x