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

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
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

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
∫[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)][0,π/4]-2[sin(x/2)+cos(x/2)][π/4,π]