令x=2sint则原式=∫(π/6→π/2)2cost*2costdt=2∫(π/6→π/2)(cos(2t)+1)dt=∫(π/6→π/2)cos(2t)d(2t)+2∫(π/6→π/2)dt=sin(2t)|(π/6→π/2)+2t|(π/6→π/2)=-√3/2+2π/3我用几何的办法又算了一下，还是这个答案啊。
2π/3-√3/2
