Should I learn trig substitution on my own or wait until calculus 3?

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Discussion Overview

The discussion revolves around whether a student currently in Calculus II should learn trigonometric substitution independently or wait until it is covered in Calculus III. Participants explore the typical placement of this topic in calculus courses and the difficulty of self-teaching it.

Discussion Character

  • Debate/contested, Homework-related, Conceptual clarification

Main Points Raised

  • One participant notes that their Calculus II course will not cover trigonometric substitution due to time constraints and questions if it is typically taught in Calculus III.
  • Another participant shares their experience of learning trigonometric substitution in high school, suggesting it is not difficult but requires memorization and practice to recognize problem-solving techniques.
  • A different participant asserts that trigonometric substitution is usually covered in Calculus II and encourages learning it over the summer, claiming it will not be addressed in Calculus III.
  • One participant expresses disbelief that a Calculus II course would not include trigonometric substitution, suggesting that the course may not be adequately rigorous for engineering or mathematics tracks.
  • Another contributor mentions that learning trigonometric substitution can be accomplished in a few hours and emphasizes the importance of also learning integration by partial fractions, which is often taught alongside trigonometric substitution.
  • One participant describes how some programs attempt to introduce basic integration techniques, including trigonometric substitution, towards the end of Calculus I or at the beginning of Calculus II, indicating variability in course structure.

Areas of Agreement / Disagreement

Participants express differing views on whether trigonometric substitution is typically taught in Calculus II or III, and there is no consensus on the necessity of self-teaching it versus waiting for formal instruction.

Contextual Notes

Some participants highlight the reliance on memorization of trigonometric identities and the potential variability in course content across different educational programs.

vinnie
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I am in calc 2 right now, and we were told we will not have time to learn trigonmetric substitution. There is a section on it in the single variable book we are using. Is trig sub usually taught in calculus 3 or should I learn it on my own? Is it a difficult concept to self-teach?
 
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I learned it in high school. Its not a difficult concept to learn, but it does take some memorization and a lot of practice in order to recognize the tricks that some problems will have.
 
Calc 2 is the typical place. Learn it over the summer. It won't be done in calc 3.
 
vinnie said:
I am in calc 2 right now, and we were told we will not have time to learn trigonmetric substitution. There is a section on it in the single variable book we are using. Is trig sub usually taught in calculus 3 or should I learn it on my own? Is it a difficult concept to self-teach?

You will not have time to learn it in your Calculus 2 course? NONSENSE! Learn it on your own. What kind of Calculus 2 course are you in? If an engineering or mathematics track course, then you are being cheated.

Basically, you are applying the pythagorean theorem and substituting from the relationship of variables and expressions based on the labeling which can be done on the triangle. This does not require much memorization, or nearly none.
 
I learned Trig Sub in Calculus II. It's really something you can cover in a few hours on your own. Make sure you learn Integration by Partial Fractions too (often included near Trig Sub in textbooks - in the sections on alternative integration techniques). If you know your Trig identities from Pre-Calculus, Trig-Sub will be a very logical method.
 
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I've seen programs that attempt to cover basic integration techniques (substitution, by parts, trig substitution) in the last weeks of Calc I. It is usually blocked in with the first sections of calc II (see above, along with basic area and volume integration).

As everyone else has said, it's mostly just basic memorization of some trig identities. Even with a few basic identities, you can usually u-substitute your way through the problem.
 

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