integral from 2 to 6 of 4/x

Lösung

\int_{2}^{6} \frac{4}{x} d x

4 ln (3)

Dezimale

4.39444 \dots

Schritte zur Lösung

\int_{2}^{6} \frac{4}{x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{2}^{6} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 4 [ln ∣ x ∣]_{2}^{6}

Berechne die Grenzen:

ln (6) - ln (2)

= 4 (ln (6) - ln (2))

Vereinfache

= 4 ln (3)

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

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

\int_{0}^{a} a^{2} - y^{2} d y

\int_{0}^{2} 28 - (3 x^{2} + 2 x + 12) d x

\int_{0}^{3} (x^{2} - 2) d x