The purpose of this video is to teach students how to evaluate line integrals of vector fields directly. This is an important skill to learn, since not every vector field is conservative. In particular, the vector field in example #3 is not conservative, and so you are incorrect -- the fundamental theorem does not apply to that example.
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These can all be solved using the fundamental theorem of line integrals
The purpose of this video is to teach students how to evaluate line integrals of vector fields directly. This is an important skill to learn, since not every vector field is conservative. In particular, the vector field in example #3 is not conservative, and so you are incorrect -- the fundamental theorem does not apply to that example.