integral from 7/2 to 8 of 3/(x-2)

Lösung

\int_{\frac{7}{2}}^{8} \frac{3}{x - 2} d x

6 ln (2)

Dezimale

4.15888 \dots

Schritte zur Lösung

\int_{\frac{7}{2}}^{8} \frac{3}{x - 2} d x

Entferne die Konstante:

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

= 3 \cdot \int_{\frac{7}{2}}^{8} \frac{1}{x - 2} d x

Wende U-Substitution an

= 3 \cdot \int_{\frac{3}{2}}^{6} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 [ln ∣ u ∣]_{\frac{3}{2}}^{6}

Berechne die Grenzen:

ln (6) - ln (\frac{3}{2})

= 3 (ln (6) - ln (\frac{3}{2}))

Vereinfache

= 6 ln (2)

\int_{1}^{2} ∣ 2 x - 3 ∣ d x

\int_{1}^{3} x^{2} e^{- x} d x

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

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

\int_{4}^{\infty} \frac{3}{x ^{5}} d x