Question

what is relationship between line integrals and arc length of curves?

Answer 1

if function you are integrating is 1 then they are the same

Answer 2

ok, what if it isn't 1?

Answer 3

then they are not the same. What line integral does is add up value of fucntion over the line that you are integration. if that function is 1 over the line, then obiviously you would just be adding up pieces of the line

Answer 4

ok, how is that different from the arc length?

Answer 5

arc lenght line integral when the function is 1

Answer 6

ok, but then how is arc length different when function is not 1?

Answer 7

i know you use the arc length to change a line integral into a double integral. Does it have something to do with that?