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Beliebt Rechnen >

integral from 3 to 4 of-log_{9}(x)

Lösung

\int_{3}^{4} - lo g_{9} (x) d x

Lösung

- 8 lo g_{9} (2) + \frac{3}{2} + \frac{1}{2 ln ( 3 )}

+1

Dezimale

- 0.56859 \dots

Schritte zur Lösung

\int_{3}^{4} - lo g_{9} (x) d x

Entferne die Konstante:

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

= - \int_{3}^{4} lo g_{9} (x) d x

Wende die partielle Integration an

= - [x lo g_{9} (x) - \int \frac{1}{2 ln ( 3 )} d x]_{3}^{4}

\int \frac{1}{2 ln ( 3 )} d x = \frac{1}{2 ln ( 3 )} x

= - [x lo g_{9} (x) - \frac{1}{2 ln ( 3 )} x]_{3}^{4}

Berechne die Grenzen:

8 lo g_{9} (2) - \frac{3}{2} - \frac{1}{2 ln ( 3 )}

= - (8 lo g_{9} (2) - \frac{3}{2} - \frac{1}{2 ln ( 3 )})

Vereinfache

= - 8 lo g_{9} (2) + \frac{3}{2} + \frac{1}{2 ln ( 3 )}

Graph

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