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a_little_demon

henry14 said:
Tính tích phan:
[TEX]\int\limits_{0}^{bi/4}sin x co s x/( sin 2x + co s 2x) dx[/TEX]
Bấm để xem đầy đủ nội dung ...

Đặt [TEX]I=\int_{0}^{\pi/4}\frac{sinxcosx}{sin2x+cos2x}dx[/TEX]
=>[TEX]8I=\int_{0}^{\pi/4}\frac{2sin2x}{sin2x+cos2x}d2x[/TEX]
<=>[TEX]8I=\int_{0}^{\pi/4}\frac{sin2x+cos2x}{sin2x+cos2x}d2x+\int_{0}^{\pi/4}\frac{sin2x-cos2x}{sin2x+cos2x}d2x[/TEX]
<=>[TEX]8I=\int_{0}^{\pi/4}d2x+\int_{0}^{\pi/4}\frac{d(sin2x+cos2x)}{sin2x+cos2x}[/TEX]
<=>[TEX]I=\frac{1}{8}(2x+ln/sin2x+cos2x/)/_0^{\pi/4}[/TEX]
=>[TEX]I=\frac{\pi}{16}[/TEX]
:):):):):):)
 
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