设Q(x,y)在xoy平面上有一阶连续偏导数,曲线积分∫L 2xydx+Q(x,y)与路径无关,对任意t恒有∫L 2xydx+Q(x,y)dy从点(0,0)到(t,1)的积分等于从点(0,0)到(1,t)的积分,求Q(x,y)令P(X,Y)=2XY积分
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![设Q(x,y)在xoy平面上有一阶连续偏导数,曲线积分∫L 2xydx+Q(x,y)与路径无关,对任意t恒有∫L 2xydx+Q(x,y)dy从点(0,0)到(t,1)的积分等于从点(0,0)到(1,t)的积分,求Q(x,y)令P(X,Y)=2XY积分](/uploads/image/z/10362286-46-6.jpg?t=%E8%AE%BEQ%EF%BC%88x%2Cy%EF%BC%89%E5%9C%A8xoy%E5%B9%B3%E9%9D%A2%E4%B8%8A%E6%9C%89%E4%B8%80%E9%98%B6%E8%BF%9E%E7%BB%AD%E5%81%8F%E5%AF%BC%E6%95%B0%2C%E6%9B%B2%E7%BA%BF%E7%A7%AF%E5%88%86%E2%88%ABL+2xydx%2BQ%EF%BC%88x%2Cy%EF%BC%89%E4%B8%8E%E8%B7%AF%E5%BE%84%E6%97%A0%E5%85%B3%2C%E5%AF%B9%E4%BB%BB%E6%84%8Ft%E6%81%92%E6%9C%89%E2%88%ABL+2xydx%2BQ%28x%2Cy%29dy%E4%BB%8E%E7%82%B9%EF%BC%880%2C0%EF%BC%89%E5%88%B0%EF%BC%88t%2C1%EF%BC%89%E7%9A%84%E7%A7%AF%E5%88%86%E7%AD%89%E4%BA%8E%E4%BB%8E%E7%82%B9%EF%BC%880%2C0%EF%BC%89%E5%88%B0%EF%BC%881%2Ct%EF%BC%89%E7%9A%84%E7%A7%AF%E5%88%86%2C%E6%B1%82Q%EF%BC%88x%2Cy%EF%BC%89%E4%BB%A4P%28X%2CY%29%3D2XY%E7%A7%AF%E5%88%86)
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