Question

点L为从点(1,1)到点(0,0)的直线段,则积分∫(x^2-y^2)dx+xy dy下限为L的值

Answer 1

设曲线L为:x=t,y=t,t从1到0,则dx=dt,dy=dt

曲线积分化为

∫（1~0）(t^2-t^2)dt+t^2dt

=∫(1~0)t^2dt

=-t^3/3