Question

Выч несоб-ый интеграл и уст расх

Answer 1

$int tgx, dx=int frac{sinx}{cosx}, dx=int frac{-d(cosx)}{cosx}=Big [; int frac{dt}{t}=ln|t|+C; Big ]=-ln|cosx|+C; ;\\\intlimits^{pi }_{frac{pi}{2}}, tgx, dx=limlimits _{varepsilon to +0}Big (-ln|cosx|Big |_{frac{pi}{2}+varepsilon }^{pi }Big )=limlimits _{varepsilon to +0}Big (-ln|cospi |+ln|cos(frac{pi}{2}+varepsilon )|Big )=\\=limlimits_{varepsilon to +0}Big (-ln|-1|+ln|-sinvarepsilon |Big )=limlimits_{varepsilon to +0}Big (-ln1+ln(sinvarepsilon )Big )=\\=-0+(-infty )=-infty ; ; ; Rightarrow ; ; ; rasxoditsya$