Advances in Energy and Integral Area Calculations

A transform function, and new additional theorem, allows work and energy, to be calculated for any constant, or time-varying force function, in integral form, as a function of time. In addition, the work W = \`{o} f(x) dx, and corresponding change in kinetic energy DK, of an object or particle, with a time-varying mass m(t), can be determined using the transform function. The individual work, and change in kinetic energy, can be calculated for the vector component(s), which make-up a resultant force function, when more than one force vector component simultaneously do work on an object or particle, along the same axis, using the transform function, and new additional theorem.