All definite integrals should be continuous on the interval (a,b). If this criteria is not met, then it becomes a improper integral. There cases of improper integrals are described below. Whenever this occurs, replace or - by a letter of your choice. Then evaluate the improper integral as the letter of your choice goes approaches or - . In this example, this represents the derivative of arctan yielding: lim d d. Only take the limit when you are plugging in the bounds. lim d d. Thus, we will take the limit as d approaches infinity. (you can use any arbitrary letter of your choice. : integrate using integration techniques. In this example, using integration by parts will yield: lim d x xe dx d. 0 x dx x xe x xe e e dx. Only take the limit when you are plugging in the bounds. lim d x x e lim d d d e.
