WORKDONE BY VARIABLE FORCE

Workdone by variable force

A body moving from xᵢ to xf under variable force. Graph shows variation of force with position.
Consider Δx=AB, The force in this interval is nearly constant 
ie; ΔW=F(x)Δx
F(x)Δx  Area of rectangle when we add successive rectangular areas, we get total work as
W = ∑ˣₓᵢ F(x)Δx
When we take Δx tends to zero the summation can be replaced integration 

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