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What is the distance a particle has moved if I know the work done 
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#1
Feb2612, 12:54 PM

P: 108

1. The problem statement, all variables and given/known data
I was asked to find the distance a particle had traveled and was given its integral solved, except the upper limit was an equation. [itex](x^2+2x)[/itex] is the force in pounds that acts on the particle 2. Relevant equations [itex]\int_{0}^{x^2+2}(x^2+2x)dx = 108[/itex] 3. The attempt at a solution I know I must find what number the top limit equation equals, but I've been inserting random numbers with no success. Also, I don't know if it is possible to find the value of x and plug it in. This is ridiculous, why couldn't they just give me the integral with the limits and I solve it. 


#2
Feb2612, 12:58 PM

P: 65

What is the integral of x^{2} + 2x?



#4
Feb2612, 02:01 PM

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P: 5,208

What is the distance a particle has moved if I know the work done
RGV 


#5
Feb2612, 04:59 PM

P: 108

Rewinding everything I know: The force exerted on the particle: [tex](x'^2+2x')[/tex] The initial point of the particle: 0 The distance traveled by the particle (that's my upper limit) given by: [tex](x^2+2)[/tex] And the total work done by the particle after traveling the distance I'm looking for: 108 Still not helps writing all that. How can I find the upper limit value or the x value to plug it in and get 108 as answer? 


#6
Feb2612, 05:38 PM

P: 65

I agree with RGV. It may be easier to think about using a different variable name for the integral than the x you're trying to solve for.
Try plugging in the limits of integration as if you are evaluating the integral. 


#7
Feb2612, 05:57 PM

P: 108

[tex] \int_{0}^{6}(x'^2+2x')dx' = 108,[/tex] However, isn't there a process to reach that? I did it by brute force. 


#8
Feb2612, 07:54 PM

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P: 5,208

RGV 


#9
Feb2612, 08:10 PM

P: 8

Here's what I did, perhaps you may find the process of some use.
1) I computed the integral and applied the limits. 2) I know that the integral with the limit substitutions = 108 3) Now it's mostly a matter of expanding the terms and factoring to find solutions. 4) The only applicable solution I found was x=2 5) The upper limit with the x=2 substitution is indeed equal to 6. Sorry for the short reply, I did it by hand and did the expansions and factoring by calculator since they were quite long. If you would like, I could write it out or post a picture of my solution if you did not understand my steps above. Hope that helps, Drood 


#10
Feb2612, 08:50 PM

P: 108




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