integral from 2 to 1 of 1/x

Lösung

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

- ln (2)

Dezimale

- 0.69314 \dots

Schritte zur Lösung

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= - [ln ∣ x ∣]_{1}^{2}

Berechne die Grenzen:

ln (2)

= - ln (2)

\int_{0}^{\frac{π}{3}} 5 sin (\frac{x}{2}) d x

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{x}{2} d x

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

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

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