please answer with calculus and not physics and show all steps

3. In physics, work is the energy transferred to or from an object via the application of force along a displacement. In simple terms, W = F - d where, W is work, F is the force, and d is the displacement. When moving an object from the point a: = a to the point a: = b with a variable force F(x) the work can be computed via the integral szabF($) dm. Consider a simple helical spring with a natural length of 0.1 m. Hook's law states that the force required to hold a spring that has been stretched :1: meters from its natural state is F (x) 2 km. The positive constant k is associated with the stiffness of the spring. Thus, it requires an increasing force to stretch the spring further and further from its natural length. (a) Consider that a force of 40 N is required to hold the spring at a length of 0.15 m. Determine the constant k: for this spring. (b) How much work is required to stretch the spring from 0.15 m to 0.2 m? (c) How much work is required to compress the spring, from its natural length, to a length of 0.05 In? Explain whether the result you found is reasonable