integral from 0 to 3 of (x^2)/(x^3+4)

Lösung

\int_{0}^{3} \frac{x ^{2}}{x ^{3} + 4} d x

\frac{1}{3} (ln (31) - 2 ln (2))

Dezimale

0.68256 \dots

Schritte zur Lösung

\int_{0}^{3} \frac{x ^{2}}{x ^{3} + 4} d x

Wende U-Substitution an

= \int_{4}^{31} \frac{1}{3 u} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{4}^{31} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{4}^{31}

Berechne die Grenzen:

ln (31) - 2 ln (2)

= \frac{1}{3} (ln (31) - 2 ln (2))

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