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Properties of the integral

  1. Apr 6, 2016 #1
    1. The problem statement, all variables and given/known data
    i am studyng, for my multivariable calculus course, and i get this integral, the problem is, i dont know how the simplify the integral that way.

    2. Relevant equations
    i will put the integral in a very HD screen shoot, yes a litle one not the entire screen calculo.png



    3. The attempt at a solution
    i used the symetrical property of definite integrals, and get stuck when i check the simplification they did in the book, i need help to know how to continue, or what property they used. i got the second line OK, then to the thirth line i got stuck
     
  2. jcsd
  3. Apr 6, 2016 #2
    you can try substitution method.
    hint convert it to sqrt(1+z^2) dz and then apply substitution.
     
  4. Apr 6, 2016 #3
    hi tanks for the answer, but if i do the sustitution how the 1/d ends out of the integral?
     
  5. Apr 6, 2016 #4
    sorry 1/p
     
  6. Apr 6, 2016 #5
    do not worry as you are integrating over x.
     
  7. Apr 6, 2016 #6
    forgot it i have done z=x/2p
    dz=1/2p
    then... 2(1/2p)=1/p outside
    now my doubt is how to make squart 4p2 + x2??????
     
  8. Apr 6, 2016 #7
    ok now i got 1/p∫√(1+z2)dz how i should proceed to make that into this 1/p∫√(4p2+x2)dx
    its like somehow, they put the (x/2p)2=x2/4p2 into a sum, but only happens in logaritm properties
     
  9. Apr 7, 2016 #8
    actually the idea is to get a standard form and then use the results from table of integrals
     
  10. Apr 7, 2016 #9

    SteamKing

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    What happens when you put ##1 + (\frac{x}{2p})^2## over a common denominator? That's the step you're missing: how to add a fraction to a whole number.
     
  11. Apr 10, 2016 #10
    Hi, so you mean 2p/2p +(x/2p)^2??
     
  12. Apr 10, 2016 #11
    thanks for reply
     
  13. Apr 10, 2016 #12

    SteamKing

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    Close, but you want to get the quantity ##(\frac{x}{2p})^2## added to 1.
     
  14. Apr 10, 2016 #13
    Well, following your previous hint, a way to add a fraction number, to a whole y should do the following: 1 + x^2/4p^2=(4p^2+x^2)/4p^2
    It's ok?
     
  15. Apr 10, 2016 #14

    SteamKing

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    That looks OK. You should be able to simplify the original integral as shown.
     
  16. Apr 10, 2016 #15
    Oh my god it was so obvious, many thanks now looks like squareroot((1/4p^2)(4p^2 +x^)
     
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