Solve the Problem $F ( x , y ) = M i + N j$

question 132

Short Answer

Solve the problem.
-a). For the field $F ( x , y ) = M i + N j$ and the closed counterclockwise plane curve $C$ in the $x y - p l a n e$ , show that
$$\int _ { C } F \cdot n d s = \int _ { C } M d y - N d x .$$
b). How would the equality change if the closed path is followed clockwise?

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