integral from-2 to 1 of 3/(4+x)

Lösung

\int_{- 2}^{1} \frac{3}{4 + x} d x

3 (ln (5) - ln (2))

Dezimale

2.74887 \dots

Schritte zur Lösung

\int_{- 2}^{1} \frac{3}{4 + x} d x

Entferne die Konstante:

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

= 3 \cdot \int_{- 2}^{1} \frac{1}{4 + x} d x

Wende U-Substitution an

= 3 \cdot \int_{2}^{5} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 [ln ∣ u ∣]_{2}^{5}

Berechne die Grenzen:

ln (5) - ln (2)

= 3 (ln (5) - ln (2))

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