The comparison test let's us deduce the convergence or divergence of some improper integrals by relating a complicated function that is challenging to a simpler one we can do. If we compare two functions f(x) greater than g(x) greater than 0, we can deduce things about the convergence of the improper integrals. If the larger integral converges from 1 to infinity, then the smaller one must as well. Likewise, if the smaller one diverges, then the bigger one diverges.

We specifically focus on integrals of 1/x^p, which we know precisely when it converges and diverges. Then if there is a more complicated rational function, we can compare it to this.

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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