Comparison Test for Improper Integrals Problem 1 (Calculus 2)

The comparison test is an important tool for improper integrals that are too difficult to evaluate directly. We go over the basics of what the comparison test says and how to find bigger/smaller functions. This one is simple but covers all of the fundamentals. More problems are linked below.
Comparison Test for Improper Integrals Problem 2: • Comparison Test for Im...
Comparison Test for Improper Integrals Problem 3: • Comparison Test for Im...
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[@manojsurya1005]

I hav a doubt in p integral in that u had put the limit as[ 1 to ∞ )but are we allowed to put the limit as [X to ∞) where X is any real number > 0 ?

[@BlackTshirtMathProfessor]

That’s correct! It’s typically the starting index of the infinite series sum. Usually this is 0 or 1.

[@manojsurya1005]

@@BlackTshirtMathProfessor but then Y did u did the second example for comparison test by splitting the integral, u could hav simply said that the lower limit could be any real number greater than 0 and say it is same as the previous one and ended the video?

[@BlackTshirtMathProfessor]

It’s due the improper integral that we’re comparing with. The integral of 1/x^3 from 0 to infinity diverges due to x = 0.

[@manojsurya1005]

@@BlackTshirtMathProfessor oh ok thanks for help👍

[@BlackTshirtMathProfessor]

You’re welcome, Manoj!