An is the of a definite integral as an endpoint of the interval of integration approaches either a specified real number or positive or negative |. Although the integral dr , the integral is da is improper. In this case, we define the improper integral as a limit dr dz lim In general, an improper integral if the limit defining it |. Thus for example dr .It is possible for an improper integral to to infinity. For instance, does not dr = lim e00 J1 da . However, there are many improper integrals which diverge in no particular direction, such as is I sin dz limit diverge exists Riemann integral converge infinity divergent improper integral not improper infinite integral oscillates definite integral converges zero