A hypothetical force is described by the equation F(x) = -a/x^3 + bx^2, where a and b are positive constants. Find an expression for the amount of work that is done by this force over the range x = 1 to x = 3.

Question

A hypothetical force is described by the equation F(x) = -a/x^3 + bx^2, where a and b are positive constants.  Find an expression for the amount of work that is done by this force over the range x = 1 to x = 3.

I am thinking to calculate the change in force and multiply it by change in distance...but what is change in distance?

bobpursley · Answer

work= INTEGRAL F(x)*dx from x=1 to 3 = INT (-a/x^3 + bx^2)dx over limits = (a/2x^2 + bx^3/3) over limits = a(1/18-1/2)+b(9-1/3) check that, I did it in my head.