例2设曲线积分∫2d+y(x)与路径无 L 关,其中具有连续的导数,且(0)=0 计算xy2dx+p(x) 0,0) R P(x, y)=xy, 2(x, y)= yop(x), aP a =(xy2)=2xy a00 ay a lyo(x)= yo(x), ax ax 积分与路径无关 aP 80 ay ax例 2 设曲线积分 +  L xy dx y (x)dy 2 与路径无 关, 其中 具有连续的导数, 且(0) = 0 , 计算 +  (1,1) (0,0) 2 xy dx y (x)dy. 解 ( , ) , 2 P x y = xy Q(x, y) = y(x), ( ) 2 , 2 xy xy y y P =   =   [ y (x)] y (x), x x Q  =    =   积分与路径无关 x Q y P   =  