定积分上限π/2下限0sin^6x/(sin^6x+cos^6x)dx
问题描述：
定积分上限π/2下限0sin^6x/(sin^6x+cos^6x)dx
答
令x=π/2-t,原积分=∫(0,π/2)cos^6t/sin^6t+cos^6tdt,这两个积分相加得π/2,所以原积分=π/4
定积分上限π/2下限0sin^6x/(sin^6x+cos^6x)dx
令x=π/2-t,原积分=∫(0,π/2)cos^6t/sin^6t+cos^6tdt,这两个积分相加得π/2,所以原积分=π/4