... change with constant rate of change, 712–714 difference between left- and right-hand sums and, 718–722 explanation of, 712 with nonconstant rate of change, 715–718 overview of, 711–712 Newton, ... integrals explanation of, 903 infinite interval of integration and, 903–907 method of comparison and, 912–914 methods to approach, 908–912 unbounded and discontinuous integrands and, 907–908 use of, 903 ... functions, 334–338 historical background of, 211 instantaneous rate of change and, 209–211, 711, 983 of inverse trigonometric functions, 703–706 limit definition of, 190, 191 local linearity and, ...