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

Question

anonymous · Answer

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

anonymous · Answer

ok, what if it isn't 1?

anonymous · Answer

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

anonymous · Answer

ok, how is that different from the arc length?

anonymous · Answer

arc lenght line integral when the function is 1

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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