令x=sint，则dx=costdt原式=∫(0,π/2) √(1-sin^2t)*costdt=∫(0,π/2) cos^2tdt=(1/2)*∫(0,π/2) (1+cos2t)dt=(1/2)*[t+(1/2)*sin2t]|(0,π/2)=(1/2)*(π/2)=π/4
