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Homework Help: Error in taking the derivative of an integral

  1. Feb 22, 2006 #1
    I know that it's 6x^2 - 2 but when I'm trying take the derivative of the integral shouldn't I have to multiply each term by -1 because the x is in the lower bound? It gives a wrong answer, so am I doing something wrong or is it just that I'm not supposed to take the opposite in this case?

    [tex]
    \[ \int_x^{-1} (2-6t^2)\,dt\]

    -1 * 2(-1 - x) - -1*6*(-1-x^3)/3


    [/tex]
     
    Last edited: Feb 22, 2006
  2. jcsd
  3. Feb 22, 2006 #2
    [tex] \int_x^{-1}(2-6t^2) dt [/tex]
    [tex] (2t -2t^3)|_x^{-1} [/tex]
     
  4. Feb 22, 2006 #3
    [tex] \int_x^{-1}(2-6t^2) dt [/tex]
    [tex] (2t -2t^3)|_x^{-1} [/tex]
    [tex] [2(-1)-2(-1)^3]-[2x-2x^3] [/tex]
    [tex] 2x^3-2x [/tex]

    -Dan
     
  5. Feb 22, 2006 #4
    In this case unfortunately I have to do it the long way using

    c*(b-a) and (b^3-a^3)/3
     
  6. Feb 22, 2006 #5
    It's the same thing, just rearrange the terms:

    [tex](2t -2t^3)|_x^{-1} = 2(-1-x)-2[(-1)^3-x^3] [/tex]

    -Dan
     
  7. Feb 23, 2006 #6

    VietDao29

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    Homework Helper

    May I suggest you NOT to give out COMPLETE solutions??? :grumpy: :grumpy: :grumpy: :grumpy:
     
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