计算曲线积分∫(0,0)(1,1)xydx+(y-x)dy，其中积分路径为
(1)y=x3；
(2)y2=x．
(1)∫(0,0)(1,1)xydx+(y-x)dy=∫01[x•x3+(x3-x)•3x2]dx =∫01(3x5+x4-3x3)dx=(1/2)x6∣01+ (1/5)x5∣01-(3/4)x4∣01=-(1/20) (2)∫(0,0)(1,1)xydx+(y-x)dy=∫01[x•√x+(√x-x)•(1/2√x)]dx =∫01[x3/2+1/2-(1/2)x1/2]dx=(2/5)x5/2∣01+ (1/2)x∣01-(1/3)x3/2∣01=-17/30
