Question

证明曲线积分与路径无关题，求大神解答！

∫(1,2)到(3,4)(6xy^2-y^3)dx+(6x^2y-3xy^2)dy。

Answer 1

P(x,y)=6xy^2-y^3，Q(x,y)=6x^2y-3xy^2

偏P/偏y=12xy-3y^2；偏Q/偏y=12xy-3y^2==>偏P/偏y=偏Q/偏y==>该曲线积分与路径无关。