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Homework Help: Intergation problem help!

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data
    How to integrate

    f du/(Gu^2-g)

    ?????


    2. Relevant equations
    not sure

    hmmm thre's the one du/(a^2+b^2)=...


    3. The attempt at a solution
    But I got a complex number.

    This is not HW. hmm just can't solve a physics problem without it
    Ps. I never learn integration
     
  2. jcsd
  3. Dec 8, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    f, g and G constants? If so either a trig substitution or partial fractions. Depends on signs. Can you be more specific?
     
  4. Dec 9, 2008 #3
    in case g,f and G are constants it can be slvd as
    f/G[1/u^2-{(g/G)^1/2}^2] du

    F/G ln[{u-(g/G)^1/2}/u+(g/G)^1/2] +C
     
  5. Dec 9, 2008 #4
    [tex]t=\int_{v_{o}}^{v_{f}} \frac{m}{\frac{1}{2}pC_{d}Av^2-mg}dv[/tex]
     
    Last edited by a moderator: Dec 13, 2008
  6. Dec 9, 2008 #5
    [tex]t=\int_{v_{o}}^{v_{f}} \frac{m}{\frac{1}{2}pC_{d}Av^2-mg}dv[\tex]

    where p C A m g are constants
     
  7. Dec 9, 2008 #6

    Mark44

    Staff: Mentor

    For some reason your tex stuff isn't rendering.
     
  8. Dec 9, 2008 #7

    Defennder

    User Avatar
    Homework Helper

    Use this slash instead of the other one to closed tex tags: /tex
     
  9. Dec 9, 2008 #8
    [tex]t=\int_{v_{o}}^{v_{f}} \frac{m}{\frac{1}{2}pC_{d}Av^2-mg}dv[/tex]


    ok thanks.
     
  10. Dec 9, 2008 #9

    Mark44

    Staff: Mentor

    Factor out all of the stuff that multiplies v^2 in the denominator as well as m in the numerator. Your integral will look like this:
    [tex]K_1 \int \frac{dv}{v^2 - K_2}[/tex]
    K_1 = 2m/(p*C_d*A) and K_2 = mg/(.5p*C_d*A)

    Now, you can do either of two things:
    1. factor the denominator and then use partial fraction decomposition to get you antiderivative.
    2. look up the resulting integral in, say, the CRC Math Tables.
     
  11. Dec 11, 2008 #10
    [tex] Let \ \ \frac{1}{2}pCA=G [/tex]
    [tex]=m\int_{vo}^{vf}\frac{1}{Gv^2-mg}dv[/tex]
    [tex]= m \int_{vo}^{vf}(\frac{\frac{1}{2\sprt{mg}}}{\sqrt{G}v-\sqrt{mg}}+\frac{\frac{-1}{2\sprt{mg}}}{\sqrt{G}v+\sqrt{mg}} dv)[/tex]
    [tex]= \frac {m}{\sqrt{mgG}} ln\ ( \ {|} \ \frac{\sqrt{G}v-\sqrt{mg}}{\sqrt{G}v+\sqrt{mg} \ {|} \ } {)} |_{vo}^{vf} [/tex]
     
    Last edited: Dec 12, 2008
  12. Dec 13, 2008 #11
    [tex]t=\int{v}^{v_{f}} {-} \frac{{1}{}pC_{d}-mg}dv[/tex]
     
  13. Dec 14, 2008 #12
    [tex] ${\displaystyle Kv_^2 = g - e^-^2^K^y \times (g-Kv_{o}^2)}$ [/tex]
     
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