原式=∫(0,1)√[(2x-x^2-1)+1]dx=∫(0,1)√[1-(x-1)^2]d(x-1)=∫(-1,0)√(1-x^2)dx令x=sint则原式=∫(-兀/2,0)cost.costdt=∫(-兀/2,0)（cos2t+1）/4d2t=∫(-兀,0)（cost+1）/4dt=0+兀/4 =兀/4 =
