integral from pi/4 to (3pi)/4 of cot(x)

Lösung

\int_{\frac{π}{4}}^{\frac{3 π}{4}} cot (x) d x

0

Schritte zur Lösung

\int_{\frac{π}{4}}^{\frac{3 π}{4}} cot (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{\frac{π}{4}}^{\frac{3 π}{4}} cos (x) csc (x) d x

Wende die partielle Integration an

= [- \int - x csc^{2} (x) d x + x cot (x)]_{\frac{π}{4}}^{\frac{3 π}{4}}

\int - x csc^{2} (x) d x = x cot (x) - ln ∣ sin (x) ∣

= [- (x cot (x) - ln ∣ sin (x) ∣) + x cot (x)]_{\frac{π}{4}}^{\frac{3 π}{4}}

Vereinfache

= [ln ∣ sin (x) ∣]_{\frac{π}{4}}^{\frac{3 π}{4}}

Berechne die Grenzen:

0

= 0

\int_{π}^{2 π} 5 sin (2 x) d x

\int_{0}^{4} 3 x d x

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\int_{0}^{4} \frac{1}{4 t ^{2} + 9} d t