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Use fundamental theorem of calculus to compute definite integral

  1. Sep 17, 2013 #1

    s3a

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    1. The problem statement, all variables and given/known data
    The problem and my (incorrect) work are typed and attached as TheProblemAndMyWorkTypedUp.jpg.

    2. Relevant equations
    Integral from a to b of f(t) = F(b) – F(a)

    3. The attempt at a solution
    As mentioned above, my work is attached as TheProblemAndMyWorkTypedUp.jpg. (The (2 – 1)^12 part “dissappeared” because d/dx (constant) = 0.)

    Could someone please help me figure out why what I did is wrong?
     

    Attached Files:

  2. jcsd
  3. Sep 17, 2013 #2

    UltrafastPED

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    Replace t with x^2; then t^2 = x^4.
     
  4. Sep 17, 2013 #3

    verty

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    I think you need to change t so that your upper limit is x. Then I think your argument will go through.
     
  5. Sep 17, 2013 #4

    s3a

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    Oh, yes, I jumped the gun with assuming it was just x on the upper limit of the integral!

    So, this (=the attachment of this reply) is how I do it, right?
     

    Attached Files:

  6. Sep 17, 2013 #5

    CAF123

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    Since the upper limit is a function of x, you have to apply chain rule. Straightforward application of FTOC can only be applied when the upper limit is just x and the lower limit a constant.
     
  7. Sep 17, 2013 #6

    s3a

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    So, is this (=the attachment of this reply) how it's done?
     

    Attached Files:

  8. Sep 17, 2013 #7

    CAF123

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    Correct :smile:
     
  9. Sep 17, 2013 #8

    s3a

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    Yay! Thank you! :)
     
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