题目
已知函数 P = P(x, y), Q = Q(x, y) 在单连通区域 D 上具有一阶连续偏导数，而 L subset D 为光滑曲线，则曲线积分 int_(L) Qdx - Pdy 与积分路径 L 无关的充要条件为____。A. (partial Q)/(partial y) - (partial P)/(partial x) = 0B. (partial Q)/(partial y) + (partial P)/(partial x) = 0C. (partial Q)/(partial x) + (partial P)/(partial y) = 0D. (partial Q)/(partial x) - (partial P)/(partial y) = 0
已知函数 $P = P(x, y)$, $Q = Q(x, y)$ 在单连通区域 $D$ 上具有一阶连续偏导数，而 $L \subset D$ 为光滑曲线，则曲线积分 $\int_{L} Qdx - Pdy$ 与积分路径 $L$ 无关的充要条件为____。
A. $\frac{\partial Q}{\partial y} - \frac{\partial P}{\partial x} = 0$
B. $\frac{\partial Q}{\partial y} + \frac{\partial P}{\partial x} = 0$
C. $\frac{\partial Q}{\partial x} + \frac{\partial P}{\partial y} = 0$
D. $\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = 0$
题目解答
答案
C. $\frac{\partial Q}{\partial x} + \frac{\partial P}{\partial y} = 0$