What is the physical meaning of line integrals in mathematics?

[rela]

Hi,

I'm greatly puzzled by the physical meaning of line integrals. Based on my understanding, the line inetgral of a scalar function is taking the integral of a function over a curve.

What does this exactly mean? I mean the physical meaning? Just find it hard to absorb and apply the rule of such inetgration.

To add on, there is also line integral of vector field. This again is something which I can't comprehend as well.

Could any kind souls out there explain the concepts to me?

Thanks in advance.

Regards
Rela

 

[lrsabug]

hello.

the prime application line integral is to calculate the work done on a particle on a force field (usually given by a function F(x,y,z)). for every infinitesimal movement of a particle BY AN EXTERNAL AGENT, there is the work done by the external agent to somewhat "negate" the effects of the force field. it's just like pushing a box against strong winds. in this case, you are the EXTERNAL AGENT, the box is the particle, and the force by the winds is the FORCE FIELD.

remember the usual work equation F*d? actually the mentioned equation is an ultra-simplified version of the line integral for the work done on a particle in a force field.

im sorry if my post doesn't completely answer ur question.

=)