integral from 50 to 100 of x/(16+8x^2)

Lösung

\int_{50}^{100} \frac{x}{16 + 8 x ^{2}} d x

\frac{1}{16} ln (\frac{1667}{417})

Dezimale

0.08660 \dots

Schritte zur Lösung

\int_{50}^{100} \frac{x}{16 + 8 x ^{2}} d x

Wende U-Substitution an

= \int_{20016}^{80016} \frac{1}{16 u} d u

Entferne die Konstante:

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

= \frac{1}{16} \cdot \int_{20016}^{80016} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{16} [ln ∣ u ∣]_{20016}^{80016}

Berechne die Grenzen:

ln (80016) - ln (20016)

= \frac{1}{16} (ln (80016) - ln (20016))

Vereinfache

= \frac{1}{16} ln (\frac{1667}{417})

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