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Improper Integrals

An integral of the form

is called an improper integral. The improper integral dx is defined by

If the limit on the right hand side exists,  dx is said to be convergent or to converge to that limit; otherwise, it is said to be divergent. Similarly, the improper integral

If this limit exists, is said to be convergent. Otherwise, it is divergent.

The improper integral is defined in terms of the first two improper integrals:

If both integrals on the right hand side are convergent, then is said to be convergent; otherwise it is divergent.

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