A variable force of pounds moves an object along a straight line when it is feet from the origin. Calculate the work done in moving the object from ft to ft.

4.5 lbs. ft

Step-by-step explanation:

Work done by a variable force in moving a distance dx is given mathematically

W = ∫ F dx where the definite integral is done over the entire distance moved by the variable force.

For this question,

F = (5x⁻²) lbs

W = ∫¹⁰₁ 5x⁻² dx = [-5x⁻¹]¹⁰₁ = [-5/x]¹⁰₁ = [-5/10] - [-5/1] = - 0.5 + 5 = 4.5 lbs. ft