integral from 0.5 to 1 of ln|x-0.5|

Lösung

\int_{0.5}^{1} ln ∣ x - 0.5 ∣ d x

- 0.84657 \dots

Schritte zur Lösung

\int_{0.5}^{1} ln ∣ x - 0.5 ∣ d x

Entferne die Extremwerte

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

Wende U-Substitution an

= \int_{0}^{0.5} ln (u) d u

Wende die partielle Integration an

= [u ln (u) - \int 1 d u]_{0}^{0.5}

\int 1 d u = u

= [u ln (u) - u]_{0}^{0.5}

Berechne die Grenzen:

- 0.84657 \dots

= - 0.84657 \dots

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