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Integration By Partial Fractions | Calculus 2 Lesson 15 - JK Math
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How to Integrate By Partial Fractions (Calculus 2 Lesson 15)
In this video we learn about how to solve integrals involving complex rational functions using a technique known as partial fractions. We learn how to identify the types of factors in the denominator that can be used to break up rational functions into simpler rational functions called “partial fractions.” These include linear factors, repeated linear factors, quadratic factors, and repeated quadratic factors. We look at examples of integrals that include these different types of factors and go through the step-by-step process of breaking them up into partial fractions that we then will be able to integrate using other previously learned integration rules techniques.
This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Why Partial Fractions?
5:17 Types of Factors
7:19 Example - Distinct Linear Factors
19:37 Example - Repeated Linear Factors
33:43 Example - Distinct Quadratic Factors
45:12 Example - Repeated Quadratic Factors
50:22 Outro
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
(Commissions earned on qualifying purchases)
Find me on social media:
Instagram: @jk_mathematics
Found this video to be helpful? Consider giving this video a like and subscribing to the channel!
Thanks for watching! Any questions? Feedback? Leave a comment!
-Josh from JK Math
#calculus
Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.
In this video we learn about how to solve integrals involving complex rational functions using a technique known as partial fractions. We learn how to identify the types of factors in the denominator that can be used to break up rational functions into simpler rational functions called “partial fractions.” These include linear factors, repeated linear factors, quadratic factors, and repeated quadratic factors. We look at examples of integrals that include these different types of factors and go through the step-by-step process of breaking them up into partial fractions that we then will be able to integrate using other previously learned integration rules techniques.
This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Why Partial Fractions?
5:17 Types of Factors
7:19 Example - Distinct Linear Factors
19:37 Example - Repeated Linear Factors
33:43 Example - Distinct Quadratic Factors
45:12 Example - Repeated Quadratic Factors
50:22 Outro
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
(Commissions earned on qualifying purchases)
Find me on social media:
Instagram: @jk_mathematics
Found this video to be helpful? Consider giving this video a like and subscribing to the channel!
Thanks for watching! Any questions? Feedback? Leave a comment!
-Josh from JK Math
#calculus
Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.
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