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Homework Help: Trig simplifycation and Intergration

  1. Oct 1, 2006 #1
    kay doing Cylidical Shells and what not.

    given y=sin(x^2)
    from x=0..sqr(pi)
    and rottated around the y-axis.

    I use the forumla for intergration

    V=2(pi)x F(x) d(x)

    i get when i subsitute

    2(pi)x Sin(x^2) d(x)
    I know since 2(pi) is constan i pull it through the intergral.
    Can I simplify : x Sin(x^2) in to something easier for integration.
     
  2. jcsd
  3. Oct 1, 2006 #2

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    Substitution.
     
  4. Oct 1, 2006 #3
    just wanna make sure i did it right.. since it's been a while since i did substition.

    for my question i woul have
    u=x^2

    du/dx=2x
    du=2x dx
    1/2(du) = x dx. which will fit into my orginal equation.
     
  5. Oct 1, 2006 #4

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    That all looks right. Make sure to change the bounds as well.
     
  6. Oct 1, 2006 #5
    kay lost me there what you mean change the bounds?
     
  7. Oct 1, 2006 #6

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    The integration goes from x=0 to x=sqrt(pi), so from u=0 to u=pi.
     
  8. Oct 1, 2006 #7
    ok.. don't understnad why i have to change my bounds... but iwill take your word for it.
     
  9. Oct 1, 2006 #8

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    Good, that's the way math should be done. Seriously, what don't you understand? If you want to integrate from x=0 to x=sqrt(pi), and you have set u=x^2, then to integrate over the same region you need to go from u=0^2=0 to u=(sqrt(pi))^2=pi.
     
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