integral from 1 to 2 of 2xln(x)

Lösung

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

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

Dezimale

1.27258 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

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

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

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