设曲线积分的路径为y=x2，则∫(0,0)(1,1)xydx+(y-x)dy=____．

设曲线积分的路径为y=x²，则∫_(0,0)^(1,1)xydx+(y-x)dy=____．
【正确答案】：1/12。解析：∫_(0,0)^(1,1)xydx+(y-x)dy=∫₀¹[x•x²+(x²-x)•2x]dx=∫₀¹(3x³-2x²)dx=(3/4)x⁴∣₀¹-(2/3)x³∣₀¹=1/12