Calculus II (Integration Methods, Series, Parametric/Polar, Vectors) Full Course - Integral Test | Derivation & 1st Example

Master Calculus II: Dive into Integrals and Infinite Series with Expert Guidance!

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28 learners

What you'll learn

Develop proficiency in integration techniques such as parts, trigonometric substitutions, and partial fractions
Apply integration methods to solve improper integrals and series approximations
Analyze parametric and polar curves for calculus problems, including areas and arc lengths
Understand complex numbers and sequences to evaluate limits and convergence tests

This course includes

7.5 hours of video
Certificate of completion
Access on mobile and TV

Summary

Keywords

Math Solution College Example integral test improper series converge diverge

Full Transcript

The Integral Test is a beautiful piece of mathematics that relates an infinite series to an improper integral. Both get interpreted geometrically, and this results in the fact that the corresponding improper integral converges or diverges precisely when the series converges or diverges. This is particularly useful when we have a complicated series we don't understand, but the corresponding function is one we know how to integrate. However, this is also the source of its main limitation: if we can't integrate the function, it just isn't helpful. **************************************************** 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