-8 lim arcsin =lim arcsin 0 2 例6证明广义积分门1当q<1时收敛,当 q≥1时发散 证(1)q=1,1 ∫nac=mx >1 q (2)q≠1, d x 0 vq q q<1  − →+       = a a x 0 0 lim arcsin       − − = →+ lim arcsin 0 0 a a   . 2  = 例 6 证明广义积分 1 0 1 dx x q 当q  1时收敛，当 q  1时发散. (1) q = 1,  1 0 1 dx x q  = 1 0 1 dx x   1 0 = ln x = +, (2) q  1,  1 0 1 dx x q 1 0 1 1       − = − q x q       − +   = , 1 1 1 , 1 q q q 证