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Calculus III - Fundamental Theorem for Line Integrals tutorial.math.lamar.edu › fundthmlineintegrals
16 нояб. 2022 г. · A path C is called closed if its initial and final points are the same point. For example, a circle is a closed path. A path C is simple if it ... |
For example, suppose that the singular point P is on the xy-plane, and suppose that our closed curve C is also on the xy-plane, as sketched below. As we shrink ... |
If C is a closed path, we can integrate around it starting at any point a; since the starting and ending points are the same, ∫C∇f⋅dr=f(a)−f(a)=0. |
4 июн. 2016 г. · From Green's theorem that ∮CFds=∬D(∂Fx∂y−∂Fy∂x)dxdy. As a result, since F is conservative, the two partial derivatives are the same, so the ... |
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