In this video, I will show you how to use the comparison test to determine if an improper integral is convergent or divergent. An improper integral is convergent if the the result of solving the integral produces a constant number, and it is divergent if the result is infinity. But sometimes it is not possible to solve the improper integral by hand, like we did in the previous video. Instead, you must use the comparison test theorem for improper integrals which takes a shortcut in four steps and the comparison test tells you if the improper integral is convergent or divergent. This is a concept which is important in Calculus 2.

I like to use the FEP-NL-SL-C acronym to remember which function is greater than which one. That means as x approaches infinity,
Factorial greater than
Exponential greater than
Polynomial (of any degree) greater than
XlogX greater than
Linear greater than
Square root (or x to the power of a constant between 0 and 1) greater than
Logarithms greater than
Constant.
I know that seems like a lot, but it is so useful to me on many exams. Let me know if this makes sense and please buy me coffee by subscribing :) It means a lot

SOLUTIONS TO THE PROBLEMS:
https://drive.google.com/file/d/1oe0eFagtY7A2nOvo4Kye4IeZT4fAseem/view?usp=sharing

In the next video, I will show you how to find the arc length of a function.

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