Question

I know Graph 1 is not conservative and Graph 2 is conservative but how can we find vector function F for Graph 2? Because F is deliberately not given.

Project 1. Fundamental theorem of line integrals amenta al theorem of line integrals: if F is a In our course we learned the conservative vector field with potential f and C is a curve connecting point A to b, then F dr f(B) f(A). Moreover it happens if and only if for any closed curve C F.dř=0. The same is true when F is a vector field defined on a graph. In this project you are given two graphs with vector fields F defined on thenm For each graph you need to determine if the defined vector field is conserva- ·To show that F is not conservative you need to find a closed curve C such on Figures 5 and 6. tive as follows that 4 6 -2 0 -2 0 Figure 5: Graph 1 2 Figure 6: Graph 2 . To show that a vector field is conservative you need to find a scalar function f such that F f If the vector field is conservative use the potential you found to check the fundamental theorem of line integrals for any curve consisting of at least 6 edges

Answer 1

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