Question

we need to determine if the vector field depicted in graph 1 and graph 2 are conservative by using the last 3 bullets points in the picture

Project 1. Fundamental theorem of line integrals In our course we learned the fundamental theorem of line integrals: if F is a 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 The same is true when F is a vector field defined on a gra In this project you are given two graphs with vector fields F defined on them 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 3 2 Figure 5: Graph 1 Figure 6: Graph 2 . To show that a vector field is conservative you need to find a scalar function fsuch that . 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. F7

Answer 1

cuttachec uiuth tta miqe enerali po ABFE ん

Now alon 月Poß月 cp 一2+1+2+3