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Trigonometric Substitution Examples | Calculus 2 - JK Math
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Example Problems For How to Use Trig Substitution to Solve Integrals (Calculus 2)
In this video we look at several practice problems of solving integrals using trigonometric substitution. In each example, we determine which trig function to substitute in (sine, secant, or tangent), and then work on rewriting the integral in terms of theta (θ) before integrating, and then switching our solution back into terms of x with the help of a reference triangle. Additionally, we look at an example of using trig substitution for a definite integral where we convert the bounds/limits of integration to be values of θ.
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 Example 1 - sqrt(2x^2-1)/x
13:34 Example 2 - 1/(x^2+1)^2
26:08 Example 3 - sqrt(4-x^2)/x^2 from sqrt(2) to 2
38:16 Outro
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
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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 look at several practice problems of solving integrals using trigonometric substitution. In each example, we determine which trig function to substitute in (sine, secant, or tangent), and then work on rewriting the integral in terms of theta (θ) before integrating, and then switching our solution back into terms of x with the help of a reference triangle. Additionally, we look at an example of using trig substitution for a definite integral where we convert the bounds/limits of integration to be values of θ.
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 Example 1 - sqrt(2x^2-1)/x
13:34 Example 2 - 1/(x^2+1)^2
26:08 Example 3 - sqrt(4-x^2)/x^2 from sqrt(2) to 2
38:16 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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