integral from 1 to 8 of 2/x

Lösung

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

6 ln (2)

Dezimale

4.15888 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 [ln ∣ x ∣]_{1}^{8}

Berechne die Grenzen:

3 ln (2)

= 2 \cdot 3 ln (2)

Vereinfache

= 6 ln (2)

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

\int_{0}^{π} \frac{1}{2} (2 θ)^{2} d θ

\int_{1}^{9} \frac{3}{t} d t

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

\int_{- 0}^{e - 1} \frac{1}{t + 1} d t