integral from 3 to 9 of |1-9/x |

Lösung

\int_{3}^{9} 1 - \frac{9}{x} d x

- 6 + 9 ln (3)

Dezimale

3.88751 \dots

Schritte zur Lösung

\int_{3}^{9} 1 - \frac{9}{x} d x

Entferne die Extremwerte

= \int_{3}^{9} - 1 + \frac{9}{x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{3}^{9} 1 d x + \int_{3}^{9} \frac{9}{x} d x

\int_{3}^{9} 1 d x = 6

\int_{3}^{9} \frac{9}{x} d x = 9 ln (3)

= - 6 + 9 ln (3)

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