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Beliebt Rechnen >

integral from 1 to 4 of ln(sqrt(x))

Lösung

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

Lösung

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

+1

Dezimale

1.27258 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{1}{2} d x = \frac{1}{2} x

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

Vereinfache

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

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

Berechne die Grenzen:

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

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

Graph

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