CONVERGENCE OF IMPROPER INTEGRALS
In this video, we'll solve six problems investigating the convergence of improper integrals. We'll work only with functions of constant sign! We'll briefly review the comparison test, but later we'll use equivalent substitution.
We'll learn how to isolate singular points and see how Taylor can be useful. We'll solve a problem where a chain of equivalences depends on a parameter and discuss the subtle situation where a constant, when replaced by an equivalent, depends on the parameter.
You'll also find a link to free materials for this video: notes and homework with answers. Here it is: https://zhestkov.online/public/course...
Even more math at my school: https://zhestkov.online
00:00 Start
01:11 Example 1 (comparison test)
02:07 Example 2 (simple equivalence)
03:38 Example 3 (equivalence and two singular points)
06:05 Example 4 (equivalence and Taylor)
08:58 Example 5 (equivalence and the role of a parameter)
12:08 Example 6 (constant depends on the parameter)
16:00 Conclusion
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