integral from pi/6 to pi/2 of cot^2(x)

Lösung

\int_{\frac{π}{6}}^{\frac{π}{2}} cot^{2} (x) d x

- \frac{π}{3} + 3

Dezimale

0.68485 \dots

Schritte zur Lösung

\int_{\frac{π}{6}}^{\frac{π}{2}} cot^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{\frac{π}{6}}^{\frac{π}{2}} - 1 + csc^{2} (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{\frac{π}{6}}^{\frac{π}{2}} 1 d x + \int_{\frac{π}{6}}^{\frac{π}{2}} csc^{2} (x) d x

\int_{\frac{π}{6}}^{\frac{π}{2}} 1 d x = \frac{π}{3}

\int_{\frac{π}{6}}^{\frac{π}{2}} csc^{2} (x) d x = 3

= - \frac{π}{3} + 3

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