integral from 2 to 3 of x/(2-x^2)

Lösung

\int_{2}^{3} \frac{x}{2 - x ^{2}} d x

\frac{1}{2} (ln (2) - ln (7))

Dezimale

- 0.62638 \dots

Schritte zur Lösung

\int_{2}^{3} \frac{x}{2 - x ^{2}} d x

Wende U-Substitution an

= \int_{- 2}^{- 7} - \frac{1}{2 u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 7}^{- 2} - \frac{1}{2 u} d u

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{- 7}^{- 2} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{2} [ln ∣ u ∣]_{- 7}^{- 2})

Vereinfache

= \frac{1}{2} [ln ∣ u ∣]_{- 7}^{- 2}

Berechne die Grenzen:

ln (2) - ln (7)

= \frac{1}{2} (ln (2) - ln (7))

\int_{1}^{2} \frac{5 - x}{8} d x

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