integral from pi/3 to pi/2 of 1/(sin(x))

Lösung

\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{1}{sin ( x )} d x

\frac{1}{2} ln (3)

Dezimale

0.54930 \dots

Schritte zur Lösung

\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{1}{sin ( x )} d x

Wende U-Substitution an

= \int_{\frac{3}{3}}^{1} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{\frac{3}{3}}^{1}

\frac{3}{3} = \frac{1}{3}

= [ln ∣ u ∣]_{\frac{1}{3}}^{1}

Berechne die Grenzen:

\frac{1}{2} ln (3)

= \frac{1}{2} ln (3)

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