0-pi-2-cos-2-t-sint-dt-

Question Number 142643 by ArielVyny last updated on 03/Jun/21

\int_{0}^{\frac{π}{2}} \frac{{c o s}^{2} t}{s i n t} d t

Answered by MJS_new last updated on 03/Jun/21

\int \frac{\cos^{2} t}{\sin t} d t = \int \frac{1 - \sin^{2} t}{\sin t} d t = \int (- \sin t + \csc t) d t =

= \cos t + \ln \tan \frac{t}{2} + C

\Rightarrow Integral {doesn}^{'} t converge

Commented by ArielVyny last updated on 03/Jun/21

i n [0 . \frac{π}{2}] i n t e g r a l d o e s n o t c o n v e r g e ?

Commented by MJS_new last updated on 03/Jun/21

yes .

Missing \left or extra \right

{[\ln \tan \frac{x}{2}]}_{0}^{π / 2} = 0 - \lim_{x \to 0^{+}} \ln \tan \frac{x}{2} but this limit {doesn}^{'} t exist

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