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Beliebt Rechnen >

integral from 0 to 1 of-ln(x)

Lösung

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

Lösung

1

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende die partielle Integration an

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

\int 1 d x = x

= - [x ln (x) - x]_{0}^{1}

Berechne die Grenzen:

- 1

= - (- 1)

Vereinfache

= 1

Graph

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