Improper integral divergence

If the limit exists, then the improper integral converges otherwise, the improper integral diverges. Given/(x) on [a,b] such that/(a) = then the improper integral is defined as... 

Maclaurin s Integral Test. Suppose Is, is a series of positive terms and/is a continuous decreasing function such that/(.r ) > 0 for 1 < x < so and/(n) = an. Then the series and the improper integral j fix) dx either both converge or both diverge. 

An improper integral has at least one infinite limit or has an integrand function that is infinite somewhere in the interval of integration. If an improper integral has a finite value it is said to converge. Otherwise it is said to diverge. 

Diverge Action of an improper integral or series with no finite value. 

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