integral from 0 to pi/2 of ln(x)

Lösung

\int_{0}^{\frac{π}{2}} ln (x) d x

\frac{π ln ( \frac{π}{2} ) - π}{2}

Dezimale

- 0.86145 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} ln (x) d x

Wende die partielle Integration an

= [x ln (x) - \int 1 d x]_{0}^{\frac{π}{2}}

\int 1 d x = x

= [x ln (x) - x]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

\frac{π ln ( \frac{π}{2} ) - π}{2}

= \frac{π ln ( \frac{π}{2} ) - π}{2}

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