∫(0,π/2)[cos(x)]^ndx=∫(0,π/2)[sin(x)]^ndx

=(n-1)/n*(n-3)/(n-2)*…*4/5*2/3,n为奇数;

=(n-1)/n*(n-3)/(n-2)*…*3/4*1/2*π/2,n为偶数。