Examples
The original definition of the Riemann integral does not apply to a function such as on the interval, because in this case the domain of integration is unbounded. However, the Riemann integral can often be extended by continuity, by defining the improper integral instead as a limit
The narrow definition of the Riemann integral also does not cover the function on the interval . The problem here is that the integrand is unbounded in the domain of integration (the definition requires that both the domain of integration and the integrand be bounded). However, the improper integral does exist if understood as the limit
Read more about this topic: Improper Integral
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