Name: Calculus II/Calculus BC - Integration by Parts: How to Recognize When it's Really a U-Sub
Uploaded: 2023-10-11T22:28:42.058Z
Duration: 3 min 59 s
Description: In this short video we see how to recognize when the integral can be solved with a u-substitution, rather than using integration by parts.

In this short video we see how to recognize when the integral can be solved with a u-substitution, rather than using integration by parts.


AP Calculus

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Calculus II/Calculus BC - Integration by Parts: How to Recognize When it's Really a U-Sub

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As an engineer, I use calculus on a daily basis to solve problems, and this includes multi-variable and vector calculus. Taking a calculus course and knowing the steps to solve a derivative or integral is one thing, but applying calculus concepts to problems in engineering and physics (i.e. biomechanics or fluid mechanics) is the true mark of understanding calculus - something I've learned how to do over many years of applying what I learned in my calculus courses.  Sure, calculus can be a challenging subject at times, but with a focus on geometric representations, attaining a solid understanding of the concepts is well within reach, and that is the way I approach the subject with my students. For example, I don't just show you how to analytically solve an integral, I show you what an integral is, and what the solution means. When you understand calculus on this level, you'll be able to work through any of the curve ball questions your teacher might throw in on an exam.

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In this video we see how to approach a polynomial division problem using the Polynomial Remainder Theorem, which cuts the time to solve down to just seconds from the minutes it would take using polynomial long-division or synthetic division. The key to acing the SAT is to recognize these types of shortcuts when they are possible!

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Calculus II/Calculus BC - Integration by Parts: How to Recognize When it's Really a U-Sub

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