integral from 0 to 1/4 of xln(4x)

Lösung

\int_{0}^{\frac{1}{4}} x ln (4 x) d x

- \frac{1}{64}

Dezimale

- 0.015625

Schritte zur Lösung

\int_{0}^{\frac{1}{4}} x ln (4 x) d x

Wende die partielle Integration an

= [\frac{1}{2} (x^{2} ln (4 x) - 2 \cdot \int \frac{x}{2} d x)]_{0}^{\frac{1}{4}}

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

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

2 \cdot \frac{x ^{2}}{4} = \frac{x ^{2}}{2}

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

Berechne die Grenzen:

- \frac{1}{64}

= - \frac{1}{64}

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