Moment of inertia, center of gravity and surface area of rotation

Abstract

The moment of inertia of a surface of rotation with respect to the axis of symmetry IX, the abscissa of its center of gravity xc, and the surface area S can be determined, as is known, in this way (see article).In computing the integrals (1), (2) and (3), both in the case of (4) and in many other cases, the technique of uniform approximation of the radical included in the subintegral functions can be used. In order to carry out such an approximation, consider the following problem (see article).