Integrating (2rx - x2)1/2 w.r.t. x and Constant r

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Homework Help Overview

The problem involves integrating the expression (2rx - x²)^(1/2) with respect to x, where r is treated as a constant. The discussion centers around integration techniques and substitutions relevant to this expression.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various integration techniques, including substitution and completing the square. There is a focus on exploring different substitutions to simplify the integration process.

Discussion Status

The discussion is active, with participants sharing their attempts and questioning each other's methods. A specific substitution involving trigonometric identities has been suggested and appears to have been effective for one participant.

Contextual Notes

Some participants are unsure about the best substitution to use, indicating a potential gap in clarity regarding the integration process. The original poster has not provided detailed attempts beyond the initial statement.

fysiikka111
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Homework Statement


Integrate
(2rx-x2)1/2
with respect to x where r is a constant.


Homework Equations





The Attempt at a Solution


Thanks
 
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What did you attempt already?
 
Integration by substitution.
 
what substitution did you try?
 
cos(x) to see if I could then use a trig identity.
 
Did you try to complete the square?
 
so
(2rx-x2)1/2=(r2-(x-r)2)1/2
 
Yes, so now it should be a lot easier...
 
I'm not sure what substitution to use.
 
  • #11
That worked, thanks a lot.
 

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