How do I solve the integral x|x|dx?

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Homework Help Overview

The problem involves evaluating the integral \(\int x|x|dx\), which requires understanding the behavior of the absolute value function in relation to the variable \(x\).

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss distinguishing cases based on the sign of \(x\), specifically \(x \geq 0\) and \(x < 0\). There is mention of straightforward calculations for each case, but the details of the integration process are not fully explored.

Discussion Status

The discussion includes various perspectives on how to approach the problem, with some participants questioning the clarity of previous responses. There is a mix of light-hearted commentary and serious inquiry, indicating an ongoing exploration of the topic.

Contextual Notes

Some participants express concern over the guidance provided, suggesting that it may not encourage independent thinking. The tone of the discussion reflects a balance between seeking help and promoting self-discovery in problem-solving.

Telemachus
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Homework Statement


I must solve [tex]\displaystyle\int_{}^{}x|x|dx[/tex]

How should I proceed?
 
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I try starting with one of the first things you learned about solving problems involving |x|.
 
You just distinguish the two cases x>=0 or x<0 and then the calculation is straighforward. in the first case you wil have the integral of x*x and in the second you will have the integral of -x*x
 
Quantumjump said:
You just distinguish the two cases x>=0 or x<0 and then the calculation is straighforward. in the first case you wil have the integral of x*x and in the second you will have the integral of -x*x

I wonder why Hurkyl didn't just say that in his reply... hmm...
I guess he doesn't know how to do it... :eek:
 
Thanks :P
 
The Chaz said:
I wonder why Hurkyl didn't just say that in his reply... hmm...
I guess he doesn't know how to do it... :eek:
Are you serious?
 
Unit said:
Are you serious?

Just guessing here, but I would say obviously no, he isn't serious. Rather it is a gentle jab at quantumjump for not giving the OP a chance to think for himself.
 
LCKurtz said:
Just guessing here, but I would say obviously no, he isn't serious. Rather it is a gentle jab at quantumjump for not giving the OP a chance to think for himself.

It was either THAT, or I was totally slamming Hurkyl (but not both)!

I prefer the Socratic method to spoon-feeding.
 

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