integral from 0 to 1 of 12xln(3x)

Lösung

\int_{0}^{1} 12 x ln (3 x) d x

12 (\frac{1}{2} ln (3) - \frac{1}{4})

Dezimale

3.59167 \dots

Schritte zur Lösung

\int_{0}^{1} 12 x ln (3 x) d x

Entferne die Konstante:

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

= 12 \cdot \int_{0}^{1} x ln (3 x) d x

Wende die partielle Integration an

= 12 [\frac{1}{2} x^{2} ln (3 x) - \int \frac{x}{2} d x]_{0}^{1}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 12 [\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2} ln (3) - \frac{1}{4}

= 12 (\frac{1}{2} ln (3) - \frac{1}{4})

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