Comparison Test for Improper Integrals
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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YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
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► Want to learn math effectively? Check out my "Learning Math" Series:
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►Want some cool math? Check out my "Cool Math" Series:
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►Check out my 2nd Channel for lower production quality "live" math videos: https://www.youtube.com/channel/UCFNL8G1CZ4dH0p-Jf7UXqdQ
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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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Видео Comparison Test for Improper Integrals канала Dr. Trefor Bazett
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.
****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************
►Full Course Playlist: CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
****************************************************
Other Course Playlists:
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
***************************************************
► Want to learn math effectively? Check out my "Learning Math" Series:
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Want some cool math? Check out my "Cool Math" Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
*****************************************************
►Check out my 2nd Channel for lower production quality "live" math videos: https://www.youtube.com/channel/UCFNL8G1CZ4dH0p-Jf7UXqdQ
*****************************************************
►Follow me on Twitter: http://twitter.com/treforbazett
*****************************************************
This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
Видео Comparison Test for Improper Integrals канала Dr. Trefor Bazett
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