Thread: grad

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?

thanks...

Originally Posted by alexandrabel90

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? Mr F says: Is the curve closed in the first example you mention ....?

can someone explain to me the properties or meaning of grad in line integrals and when can they be used?

thanks...

..