im confused over the property of line integrals..
i was reading an example in my book and for one question, it states that since the vector field is a gradient, the integral does not depend on the given parametrisation C in the question. instead we can just integrate over the line segment that connects the 2end points tgt.
while another example said, although the vector field is not a gradient, part of it is a gradient. since we are integrating over a closed curve, the contribution of the gradient is 0.
from the second para, if the contribution of the grad =0, then wont the answer for the first para be 0 since it is a grad?
can someone explain to me the properties or meaning of grad in line integrals and when can they be used?