integral from 6 to 8 of (50x)/(x^2+2)

Lösung

\int_{6}^{8} \frac{50 x}{x ^{2} + 2} d x

25 ln (\frac{33}{19})

Dezimale

13.80171 \dots

Schritte zur Lösung

\int_{6}^{8} \frac{50 x}{x ^{2} + 2} d x

Entferne die Konstante:

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

= 50 \cdot \int_{6}^{8} \frac{x}{x ^{2} + 2} d x

Wende U-Substitution an

= 50 \cdot \int_{38}^{66} \frac{1}{2 u} d u

Entferne die Konstante:

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

= 50 \cdot \frac{1}{2} \cdot \int_{38}^{66} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 50 \cdot \frac{1}{2} [ln ∣ u ∣]_{38}^{66}

Vereinfache

50 \cdot \frac{1}{2} [ln ∣ u ∣]_{38}^{66} : 25 [ln ∣ u ∣]_{38}^{66}

= 25 [ln ∣ u ∣]_{38}^{66}

Berechne die Grenzen:

ln (66) - ln (38)

= 25 (ln (66) - ln (38))

Vereinfache

= 25 ln (\frac{33}{19})

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