An improper integral is an integral where either the upper or lower limit of integration is infinite, or the integrand has a discontinuity at some point within the limits of integration.
An improper integral converges if the limit of the integral as the upper or lower limit of integration approaches a finite number exists. This can be determined using various tests such as the comparison test, limit comparison test, or the integral test.
A convergent improper integral is one where the limit of the integral is a finite number, while a divergent improper integral is one where the limit does not exist or is infinite.
Yes, an improper integral can have both upper and lower limits of integration be infinite, as long as the limit of the integral as both limits approach a finite number exists.
If an improper integral converges, its value is equal to the limit of the integral as the limits of integration approach a finite number. If it diverges, its value cannot be determined as the limit does not exist.