integral from 3 to 6 of 9/x

Lösung

\int_{3}^{6} \frac{9}{x} d x

9 ln (2)

Dezimale

6.23832 \dots

Schritte zur Lösung

\int_{3}^{6} \frac{9}{x} d x

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 9 [ln ∣ x ∣]_{3}^{6}

Berechne die Grenzen:

ln (6) - ln (3)

= 9 (ln (6) - ln (3))

Vereinfache

= 9 ln (2)

\int_{- 1}^{1} (x^{4} + x^{2}) d x

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\int_{- π}^{π} x cos^{2} (x) d x