“ If the axes of x, y, z are a right-handed system, we have Stokes’s theorem in the form
where the integral on the left is taken round the curve s in the chosen sense. When the axes are left-handed, we may either reverse the sense of l, m, n and maintain the formula, or retain the sense of l, m, n and change the sign of the right-hand member of the equation. For the validity of the theorems of Green and Stokes it is in general necessary that the functions involved should satisfy certain conditions of continuity. ”

“ The formal definition of an integral, the theorem of the existence of the integral for certain classes of functions, a list of classes of “integrable” functions, extensions of the notion of integration to functions which become infinite or indeterminate, and to cases in which the limits of integration Integral calculus. become infinite, the definitions of multiple integrals, and the possibility of defining functions by means of definite integrals—all these matters have been considered in Function. ”

“ The integration of a rational function is generally effected by resolving the function into partial fractions, the function being first expressed as the quotient of two rational integral functions. Corresponding to any simple root of the denominator there is a logarithmic term in the integral. If any of the roots of the denominator are repeated there are rational algebraic terms in the integral. ”