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

Lösung

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

- ln (2)

Dezimale

- 0.69314 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- 1}^{- \frac{1}{2}}

Berechne die Grenzen:

- ln (2)

= - ln (2)

\int_{0}^{2 - x - y} 1 d z

\int_{- 1}^{4} 6 x^{2} - x^{3} - 5 x d x

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

\int_{1}^{6} (x^{2} - 7 x + 6) d x

\int_{- 0.5}^{0} x ln (x + 1) d x