integral from 0 to 1 of ln(x^2)

Lösung

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

- 2

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int 2 d x = 2 x

= [x ln (x^{2}) - 2 x]_{0}^{1}

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

= [2 x ln (x) - 2 x]_{0}^{1}

Berechne die Grenzen:

- 2

= - 2

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