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

Lösung

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

\frac{1}{3} ln (5)

Dezimale

0.53647 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{10} \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_{2}^{10} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{2}^{10}

Berechne die Grenzen:

ln (10) - ln (2)

= \frac{1}{3} (ln (10) - ln (2))

Vereinfache

= \frac{1}{3} ln (5)

\int_{1}^{\infty} \frac{2}{3 x + 1} d x

\int_{0}^{\infty} e^{- y} y d y

\int_{0}^{4} (x^{2} - 2 x + 1) d x

\int_{- 2}^{2} (17 - ∣ x ∣^{3}) d x

\int_{1}^{5} x^{2} - x - 6 d x