Final answer:
Work done is calculated as the integral of the force with respect to displacement, represented by W = ∫ F dx, and signifies the area under the force versus displacement graph. It is not a derivative, summation, or integral with respect to time.
Step-by-step explanation:
To calculate the work done using calculus, we focus on the integral of the force with respect to displacement. The work done by a force during a displacement is defined as the integral of the force along the path of the displacement. The infinitesimal work dW done by a force F over an infinitesimal displacement dx is given by dW = Fxdx + Fydy + Fzdz, where Fx, Fy, Fz are the components of the force and dx, dy, dz are the components of the displacement.
For a constant force F acting along the direction of displacement, the work done W is simply Fd cos θ, where θ is the angle between the force and the direction of displacement.
When the force varies, the total work done is calculated by integrating the force along the path of displacement, which is not the derivative of force with respect to distance, nor is it the summation of force and distance or the integral of force with respect to time.
For one-dimensional motion, work is defined as W = ∫ F dx, which represents the area under the curve of a force versus displacement graph. If the force is variable, the integral takes into account the changes in magnitude of the force over the displacement.