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

Lösung

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

\frac{1}{3} (ln (11) - ln (3))

Dezimale

0.43309 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{3}^{11} \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_{3}^{11} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{3}^{11}

Berechne die Grenzen:

ln (11) - ln (3)

= \frac{1}{3} (ln (11) - ln (3))

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