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Decide the center of mass

  1. Mar 12, 2013 #1

    Pir

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    1. The problem statement, all variables and given/known data

    2. Relevant equations
    [tex]X_{T} = \frac{1}{m}\int_{K}^{} x dm[/tex]


    3. The attempt at a solution
    I have decided a) and I got the volume to be ∏ volume units. I need help with b).

    I try to use the formula and I get this:

    [tex]X_{T} = \frac{1}{\pi}\int_{K}^{} 3\pi x sin^2xcosx dx[/tex]

    But I need help how to solve this integral (if it's correct?). Please help me with this, how do I solve this integral?
     
  2. jcsd
  3. Mar 12, 2013 #2

    Dick

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    Did you try integration by parts?
     
  4. Mar 12, 2013 #3

    Pir

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    Is that formula correct to begin with?

    I tried integrating by parts but I couldn't solve it. Please help by writing how to do it. I have a test in two days and I need to know how to solve this before then and it takes forever if I have to ask for one step at a time when there might be several questions.
     
  5. Mar 12, 2013 #4

    Dick

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    Yes, it looks correct. Try parts using u=x dv=sin(x)^2*cos(x)dx.
     
  6. Mar 12, 2013 #5

    Pir

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    I don't understand, please write how to do it. You mean substitute x with u? That doesn't really change anything, there are still three factors.
     
  7. Mar 12, 2013 #6

    Dick

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    No, I mean do integration by parts with those as the parts. ##\int u dv=uv-\int v du##. That's integration by parts.
     
  8. Mar 12, 2013 #7

    Pir

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    wrong
     
    Last edited: Mar 12, 2013
  9. Mar 12, 2013 #8

    Pir

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    What happens with the pi?

    And why isn't the x integrated with the rest? Shouldn't it be 1/2 x^2?
     
  10. Mar 12, 2013 #9

    Dick

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    You can just factor out the constants like 3 and pi. And it doesn't sound like you done integration by parts before. There are some examples here: http://en.wikipedia.org/wiki/Integration_by_parts Start from u=x and dv=sin(x)^2*cos(x)dx. Try to figure out what v is by integrating dv.
     
  11. Mar 12, 2013 #10

    Pir

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    Yes the pi can be factored out but DID YOU NOTICE THAT THERE'S ALSO A 1/PI, DICK? What happens with that?
     
  12. Mar 12, 2013 #11

    Dick

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    I told you. Keep track of the constants separately. I'm trying to show you how to integrate x*sin(x)^2*cos(x). The constants are the easy part.
     
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