How Do You Apply Trigonometric Substitution to Integrate Sqrt(X^2 + 9)?

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SUMMARY

The discussion focuses on applying trigonometric substitution to evaluate the integral of Sqrt(X^2 + 9). The user correctly identifies the substitution x = 3sin(u) and dx = 3cos(u) as a starting point for solving the integral. The conversation highlights the importance of understanding trigonometric identities and substitution techniques in calculus, particularly for integrals involving square roots of sums of squares. A recommended resource for further learning is provided, specifically a tutorial on trigonometric substitutions.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with trigonometric identities
  • Knowledge of substitution methods in integration
  • Basic skills in solving trigonometric equations
NEXT STEPS
  • Study the method of trigonometric substitution in detail
  • Practice integrating functions using the substitution x = a sin(u)
  • Explore the use of integration by parts in conjunction with trigonometric substitution
  • Review additional resources on calculus, such as the tutorial at http://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx
USEFUL FOR

Students learning calculus, particularly those struggling with integration techniques, and educators seeking to provide clearer explanations of trigonometric substitution methods.

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Homework Statement


Evaluate the Integral: Sqrt[(X^2)+9]

Homework Equations


I know its an Integration By parts problem, but I don't know how to start it.


The Attempt at a Solution



Im JUST learning this as I type this problem out, I've just been stuck on it for a while and my book does a horrible job of explaining how to do problems. If anybody could explain the Trigonometric substitution technique or knows of a good website that explains it I would be very grateful.

For this problem though, all I did was set x=3sin(u) and dx=3cos(u).

I don't know if that's right though, because like I said, I just "learned" this yesterday
 
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