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Integrate sqrt(xx^2) 
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#1
Dec2912, 03:58 PM

P: 333

1. The problem statement, all variables and given/known data
Integrate [tex]\sqrt{xx^2}[/tex] The attempt I did a trig substitution, letting [tex]cos(\theta)=\frac{x}{sqrt(x)}[/tex] and after some manipulation ended up with [tex]2\int \ sin(\theta)cos(\theta)sin(\theta)cos(\theta) d\theta[/tex] which I have no idea how to integrate. If I make a usubstitution and let u=cos(theta) rather than simplify to get the above, I get [tex]2\int \ u\sqrt{u^2u^4}du[/tex] which I cant make any progress on either. 


#2
Dec2912, 04:19 PM

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#3
Dec2912, 04:51 PM

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The more common way to do a problem like this is to complete the square inside the radical then substitute. I think it goes a bit easier that way.



#4
Dec2912, 05:18 PM

P: 333

Integrate sqrt(xx^2)
@haruspex: Yeah, I tried that and when I got the incorrect answer, I went back and saw that I overlooked the fact that you need to insert the modulus wheen rooting a square. Will try again in case I made an error though.
@Dick: Thanks, I'll see where I can get with that. 


#5
Dec2912, 07:06 PM

P: 584

Like Dick said. Look at it like this try to reformulate it so you get something like this:
[tex]\int\sqrt{\frac{1}{4}(x}\frac{1}{2})^{2}dx[/tex] and substitute u : [tex]u=x\frac{1}{2};dx=du[/tex] and see what you can get. 


#6
Dec3012, 06:16 AM

P: 1,107

try factorizing out the x... then use a substitution sqrt x = something... simplifies things alot!



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