∫√(1-sinx)dx
=∫√[(cosx/2)^2+(sinx/2)^2-2sinx/2*cosx/2)]dx
=∫√(cosx/2-sinx/2)^2dx
=∫(cosx/2-sinx/2)dx+∫(sinx/2-cosx/2)dx
=2∫(cost-sint)dt+2∫(sint-cost)dt……(t=x/2)
=2(√2-1)-2(1-√2)
=4(√2-1)
∫√(1-sinx)dx
=∫√[(cosx/2)^2+(sinx/2)^2-2sinx/2*cosx/2)]dx
=∫√(cosx/2-sinx/2)^2dx
=∫(cosx/2-sinx/2)dx+∫(sinx/2-cosx/2)dx
=2∫(cost-sint)dt+2∫(sint-cost)dt……(t=x/2)
=2(√2-1)-2(1-√2)
=4(√2-1)