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Integral of a sqrt of polynomial

  1. Mar 23, 2009 #1
    1. The problem statement, all variables and given/known data
    (1/sqrt(x^2+16), x, 0, 4);


    2. Relevant equations
    x=4tan(theta)
    dx=4sec^2(theta)d(theta)


    3. The attempt at a solution
    (1/sqrt(16+(4tan(theta))^2)(4sec^2theta) Im confused can i get some help??
     
  2. jcsd
  3. Mar 23, 2009 #2

    AEM

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    Re: Intergrals

    If you remember that

    [tex] 1 + tan^2 \theta = sec^2 \theta [/tex]

    then you'll find that the integrand simplifies quite nicely. Don't forget to change your integration limits appropriately.
     
  4. Mar 23, 2009 #3
    Re: Intergrals

    ok, i got ln(4/sqrt(x^2 +16) + (x/4)???? is this right??????
     
  5. Mar 23, 2009 #4

    lanedance

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    Homework Helper

    Re: Intergrals

    hmmm.... if this is a definite you don't need to try and convert back to x's, just change the integration limits when you make the variable change
     
  6. Mar 24, 2009 #5

    AEM

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    Re: Intergrals

    I think that's pretty close. As the previous post mentions, I didn't change back to the x's but worked with theta limits of 0 to pi/4.
     
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