Integrating a polynomial with a square root

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SUMMARY

The discussion focuses on integrating the function (4x - x^2)^(1/2) dx. Participants recommend completing the square under the square root and applying trigonometric substitution as effective methods for solving the integral. The integration technique of trigonometric substitution is emphasized as crucial for those unfamiliar with it. Overall, the integration process is confirmed to be successful when these methods are applied correctly.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically integration.
  • Familiarity with completing the square in algebra.
  • Knowledge of trigonometric identities and substitutions.
  • Experience with integral calculus techniques.
NEXT STEPS
  • Study the method of completing the square in polynomial expressions.
  • Learn about trigonometric substitution techniques for integrals.
  • Practice integrating functions involving square roots and polynomials.
  • Explore advanced integration techniques, including integration by parts and partial fractions.
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus and integration techniques, will benefit from this discussion.

ande
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Poster has been reminded to show their work when asking schoolwork questions
1. Integrate the following: (4x - x^2)^1/2 dx 2. Any assistance would be appreciated.3. Honestly don't know where to start.
 
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Complete the square under the root, and use a trig substitution.
 
Read up on trig substitution. I hadn't covered it yet. Thank you. Works like a charm.
 
Well done.
 

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