Question

when we say work done=integral Fdx,within limits x1 and x2 how are we substituting the values of x1 and x2 in the w=Fdx expression considering x^0...i mean i can understand the intention but isnt it a bit vague to substitute any displacement value into dx?

Answer 1

i mean for spring force,F=Kx where x is displacement i understand that x is changing continuously but when when we integrate it within limits x1 and x2....we substitute their respective values to get (1/2kX^2)-(1/2kx^2)...but isnt this concept a bit vague?

Answer 2

Work is a path function not an exact differntial and substitution of x1 and x2 are done in the evaluated definite integral.