integral from 4 to 6 of x/(4x^2+8)

Lösung

\int_{4}^{6} \frac{x}{4 x ^{2} + 8} d x

\frac{1}{8} ln (\frac{19}{9})

Dezimale

0.09340 \dots

Schritte zur Lösung

\int_{4}^{6} \frac{x}{4 x ^{2} + 8} d x

Wende U-Substitution an

= \int_{72}^{152} \frac{1}{8 u} d u

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int_{72}^{152} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{8} [ln ∣ u ∣]_{72}^{152}

Berechne die Grenzen:

ln (152) - ln (72)

= \frac{1}{8} (ln (152) - ln (72))

Vereinfache

= \frac{1}{8} ln (\frac{19}{9})

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