integral from pi/6 to pi/3 of 1/(sin(x))

Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{1}{sin ( x )} d x

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

Dezimale

0.76765 \dots

Schritte zur Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{1}{sin ( x )} d x

Wende U-Substitution an

= \int_{2 - 3}^{\frac{3}{3}} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{2 - 3}^{\frac{3}{3}}

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

= [ln ∣ u ∣]_{2 - 3}^{\frac{1}{3}}

Berechne die Grenzen:

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

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

\int_{3}^{4} x - 3 d x

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

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

\int_{0}^{1} 1 e^{- s t} d t

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