Explain work done by a variable force.

Explanation

Suppose a body is acted upon by a variable force F along x-axis.
Due to this force, body is displaced from `x_i` to `x_f` , The variation of F(x) with x is shown in fig

The displancement can be divided into a large number of smell equal displacement `Deltax`. During `Deltax`. force F can be taken to contant . Then the work done is
`dW = F Deltax = ` Area of rectangle `PQRS `
Total work done is given by
`W = Lim_(Deltax to 0) sum_(x_i)^(x_f) F Deltax = int_(x_i)^(x_f) F Deltax`.
Hence, for a varying force work done is equal to definite integral of force over given displacement.