I understand the computation behind line integrals and their proof\'s, but I\'m
ID: 3346851 • Letter: I
Question
I understand the computation behind line integrals and their proof's, but I'm having trouble understanding what they really represent.
This is what I have concluded so far...
Line integrals can be a two dimensional area that is produced by some curve (in two dimensions or in space).
Line integrals in a vector field represent some work done inorder trace out an area produced by some curve.
Green's theorem is used to calculate line integrals of a simple closed curve, so we are figuring out the work done to trace out some closed loop.
Explanation / Answer
A line integral in vector calculus can be thought of as a measure of the total effect of a given field along a given curve.
More specifically, the line integral over a scalar field can be interpreted as the area under the field carved out by a particular curve
Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. YES IT IS used to calculate line integrals of a simple closed curve, so we are figuring out the work done to trace out some closed loop