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

Lösung

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

3 ln (\frac{3}{2})

Dezimale

1.21639 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{2} \frac{1}{x + 4} d x

Wende U-Substitution an

= 3 \cdot \int_{4}^{6} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 [ln ∣ u ∣]_{4}^{6}

Berechne die Grenzen:

ln (6) - 2 ln (2)

= 3 (ln (6) - 2 ln (2))

Vereinfache

= 3 ln (\frac{3}{2})

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

\int_{1}^{e} t ln (t) d t

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

\int_{0}^{\frac{π}{4}} (2 cos (x) + 1) d x

\int_{0}^{1} x (\frac{3}{2} x^{2} + \frac{1}{2}) d x