giup to voj

H

hoanghondo94

[TEX]\int_{\frac{\pi }{4}}^{\frac{\pi }{2}}\frac{xcosx}{sin^3x}dx[/TEX]
Bấm để xem đầy đủ nội dung ...

Mình giúp bạn nhé :) :p:p

[TEX]Dat \ \{u = x \\ dv = \frac{{\cos x}}{{{{\sin }^3}x}}dx \Rightarrow \{ du = dx \\ v = - \frac{1}{{2{{\sin }^2}x}}[/TEX]

Khi đó:

[TEX]I=\int\limits_{\frac{\pi }{2}}^{\frac{\pi }{4}} {\frac{{x\cos x}}{{{{\sin }^3}x}}dx} \\\\ = - \left. {\frac{x}{{2{{\sin }^2}x}}} \right|_{\frac{\pi }{2}}^{\frac{\pi }{4}} + \frac{1}{2}\int\limits_{\frac{\pi }{2}}^{\frac{\pi }{4}} {\frac{{dx}}{{{{\sin }^2}x}}} = - \left. {\frac{x}{{2{{\sin }^2}x}}} \right|_{\frac{\pi }{2}}^{\frac{\pi }{4}} - \left. {\frac{1}{2}\cot gx} \right|_{\frac{\pi }{2}}^{\frac{\pi }{4}}[/TEX] :p:p:p:p
 
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