calculus of variations

The calculus of variations is an extension of calculus concerned with the examination of definite integrals and the calculation of their maximization and minimum values. One of its most famous problems was the brachistochrone problem, in which it was required to find out the least time taken for a particle to fall, under the influence of gravity alone, between two points at different heights though not vertically above each other. The path is in fact a cycloid, the solution involving minimization of the integral that expresses the path. An example of a problem involving calculus of variations is to find the shape of a cable suspended from both ends (see catenary).