Solving Integral Problem: x(x2-4)1/2dx

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Discussion Overview

The discussion revolves around solving the integral \(\int x(x^2-4)^{1/2}dx\). Participants explore different methods for evaluating this integral, including integration by parts and substitution techniques.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in solving the integral and is unsure of the appropriate method to use.
  • Another participant suggests using the substitution \(y = x^2 - 4\) and provides the differential \(dy = 2xdx\) to simplify the integral.
  • A different participant mentions that integration by parts could be a possible method but suggests that substitution is more suitable for this problem.
  • The original poster acknowledges the suggestion of u-substitution and expresses gratitude for the reminder.

Areas of Agreement / Disagreement

There is no explicit consensus on the best method to solve the integral, but multiple participants agree that substitution is a more straightforward approach compared to integration by parts.

Contextual Notes

Participants do not clarify the limitations of their suggested methods or any assumptions that may affect the integral's evaluation.

evilq17
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I am having problems figuring out how to do this integral.
[tex]\int[/tex]x(x2-4)1/2dx

I know what the answer is, but I am not sure how to get there. I am not sure if there is a method or if you just need to do it by logic. I tried integration by parts but I just can't get to something I can integrate.

Thanks.
 
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try y=x2-4. Then dy=2xdx. Now you are left with integrating (y1/2)/2. You should be able to do that.
 
You probably COULD do it by parts? But that's clearly overkill. Like mathman pointed out, this screams u-subst.
 
Thanks. U substitution. Its been too long since I have done this. Thanks.
 

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