integral from 9 to 1 of 1/x

Lösung

\int_{9}^{1} \frac{1}{x} d x

- 2 ln (3)

Dezimale

- 2.19722 \dots

Schritte zur Lösung

\int_{9}^{1} \frac{1}{x} d x

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

= - \int_{1}^{9} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= - [ln ∣ x ∣]_{1}^{9}

Berechne die Grenzen:

2 ln (3)

= - 2 ln (3)

\int_{1}^{x} t^{2} - t d t

\int_{1}^{e} \frac{10 ln ( x )}{x} d x

\int_{0}^{x} \frac{5}{1 + 5 x ^{2}} d x

\int_{1}^{0} 3 e^{x} d x

\int_{a}^{10 b} 2 s d s