Note, however, that each integral of the following set is proper: The integrand, in every example above, is defined at each number on the interval
of integration.
Improper integrals of class (1), where the interval is not bounded, are handled
as limits: ,
where f is continuous on [a,b]. If the limit on the right exists, the improper
integral on the left is said to converge to this limit; if the limit on the right fails to
exist, we say that the improper integral diverges (or is meaningless).
The evaluation of improper integrals of class (1) is illustrated in Examples 17–
23.
Example 17 __
Find .SOLUTION: . The given integral
thus converges to 1. In Figure N7–22 we interpret as the area above the x-
axis, under the curve of y = 3, and bounded at the left by the vertical line x = 1.