积分计算 ∫(上限π下限0)(1-sinx)^(1/2) dx

题目

积分计算 ∫(上限π下限0)(1-sinx)^(1/2) dx
∫根号下(1-sinx)根号结束dx 积分上限派下限0

答案

∫[0,π]√(1-sinx) dx＝∫[0,π]√(sin^2(x/2)+cos^2(x/2)-2sin(x/2)cos(x/2)) dx=∫[0,π]√[（sin(x/2)-cos(x/2)]^2dx=∫[0,π/4][cos(x/2)-sin(x/2)]dx+∫[π/4,π][sin(x/2)-cos(x/2)]dx=2[sin(x/2)+cos(x/2)][...