Tính tích phân \(\int\limits_{\dfrac{\pi }{4}}^{\d...

C

- Hướng dẫn giải

Ta có: $\int\limits_{\dfrac{\pi }{4}}^{\dfrac{\pi }{2}} {\cot x\,dx}  = \int\limits_{\dfrac{\pi }{4}}^{\dfrac{\pi }{2}} {\dfrac{{\cos x}}{{\sin x}}\,dx}$

$= \int\limits_{\dfrac{\pi }{4}}^{\dfrac{\pi }{2}} {\dfrac{1}{{\sin x}}\,d\left( {\sin x} \right)}$

$= \ln \left| {\sin x} \right|\left| {_{\dfrac{\pi }{4}}^{\dfrac{\pi }{2}}} \right. =  - \ln \dfrac{{\sqrt 2 }}{2}.$