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Definitive Integral any ideas

  1. Aug 12, 2013 #1
    Any ideas how to solve this
    [tex]\int_0^h {\frac{1}{\sqrt{1+(r({\frac{1}{z}}-{\frac{1}{h}}))^2}}}\,dz[/tex]
    Don't have an idea from where to begin
     
    Last edited: Aug 12, 2013
  2. jcsd
  3. Aug 12, 2013 #2

    SteamKing

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    The correct term is 'definite integral'.

    Is r a constant?
     
  4. Aug 12, 2013 #3
    Yeah, this is problem from ED R is radius and h is height of cone.
     
  5. Aug 12, 2013 #4

    LCKurtz

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    Start by simplifying the integrand.
     
  6. Aug 12, 2013 #5
    How about this: We have the expression:

    [tex]\frac{1}{\sqrt{1+(r/z-a)^2}}[/tex]

    now, can you simplify that and get:

    [tex]\frac{z}{\sqrt{Q(z)}}[/tex]

    where [itex]Q(z)[/itex] is a quadratic polynomial in z? Then we'd have:

    [tex]\int \frac{z}{\sqrt{Q(z)}} dz[/tex]

    Now I don't know about you, but I'd look in my Calculus text book about integrands with radicals with quadratic expressions (I did). And what is the first thing done when that happens?
     
    Last edited: Aug 12, 2013
  7. Aug 12, 2013 #6
    That worked but solution is messy.
     
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