[Toán 12] Tích phân 12

T

truongduong9083

Gợi ý:
Chứng minh $I = \int\limits_{0}^{\dfrac{\pi}{2}}\dfrac{cos^3x}{sinx+cosx}dx = \int\limits_{0}^{\dfrac{\pi}{2}}\dfrac{sin^3x}{sinx+cosx}dx$
Nên $I = \dfrac{1}{2}\int\limits_{0}^{\dfrac{\pi}{2}}\dfrac{sin^3x+cos^3x}{sinx+cosx}dx = \dfrac{1}{2}\int\limits_{0}^{\dfrac{\pi}{2}}(1-\dfrac{sin2x}{2})dx$
 
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