Simplifying and Integrating √(1+4t^2) | Homework Help

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SUMMARY

The discussion focuses on simplifying and integrating the expression √(1+4t²). It concludes that while simplification may not be necessary, the expression is well-suited for trigonometric substitution techniques. The participants emphasize the effectiveness of using trigonometric identities to facilitate integration, particularly when dealing with constants added to squares.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with integration techniques
  • Knowledge of trigonometric substitution methods
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study trigonometric substitution for integrals
  • Learn about integration techniques involving square roots
  • Explore examples of integrating expressions with constants and squares
  • Review the properties of trigonometric functions in calculus
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques, and educators seeking to enhance their teaching methods for trigonometric substitution.

jimbo71
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Homework Statement


sqrt(1+4t^2)


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The Attempt at a Solution


I'm not sure if this even can be simplified. If it can't be how would I integrate it?
 
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Why would you want to simplify it? It's already perfectly set up for trig substitution.
 
Hi jimbo71! :smile:

Hint: whenever you see a constant ± a square, it usually helps to try a trig substitution. :wink:
 

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