integral from 50 to 100 of x/(23+9x^2)

Lösung

\int_{50}^{100} \frac{x}{23 + 9 x ^{2}} d x

\frac{1}{18} (ln (90023) - ln (22523))

Dezimale

0.07697 \dots

Schritte zur Lösung

\int_{50}^{100} \frac{x}{23 + 9 x ^{2}} d x

Wende U-Substitution an

= \int_{22523}^{90023} \frac{1}{18 u} d u

Entferne die Konstante:

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

= \frac{1}{18} \cdot \int_{22523}^{90023} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{18} [ln ∣ u ∣]_{22523}^{90023}

Berechne die Grenzen:

ln (90023) - ln (22523)

= \frac{1}{18} (ln (90023) - ln (22523))

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