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Calculus Integration from -10 to 0 Yields a Strange Result

  1. Sep 22, 2012 #1
    Calculus Integration from -10 to 0 Yields a Strange Result [RESOLVED]

    As part of a far greater enquiry, I found myself integrating:

    [itex]\int^{0}_{-10}x^3+2dx[/itex]

    So, I began integrating the [itex]x^3+2[/itex] component, yielding the result of:

    [itex][\frac{x^4}{4}+2x]^{0}_{-10}[/itex]

    Which can then be set out as a subtraction, by:

    [itex][\frac{0^4}{4}+2(0)]-[\frac{-10^4}{4}+2(-10)][/itex]

    The left term of the subtraction results in zero, whereas the right results in -2520, thus yielding the overall answer of:

    [itex]0--2520=0+2520=2520[/itex]

    However, a most curious thing occurs, when I integrate the same definite integral on my calculator -- I get a different answer:

    [itex]-2480[/itex]

    Not only can an area not be negative, but it defies my previous answer. So, now I have been lead to no other choice, but to ask you all for help, as to seeing where I went wrong.

    Thankyou in advance, mes amis.

    NOTE: I have a strong feeling that the mistake lies in either my own fault, or in my own lack of knowledge.
     
    Last edited: Sep 22, 2012
  2. jcsd
  3. Sep 22, 2012 #2
    (-10)4 ≠-104
     
  4. Sep 22, 2012 #3
    Ah bon!

    But my problem still stands, in that the result is that of a negative value -- should I just ignore the negative sign, and conclude that I must calculate the absolute value of integrals like this in future?

    EDIT: To treat the integral maybe, as so:

    [itex]|(\int^{0}_{-10}x^3+2dx)|[/itex]
     
    Last edited: Sep 22, 2012
  5. Sep 22, 2012 #4
    no, it does not.
     
  6. Sep 22, 2012 #5
    You're very correct in your declarative statement -- I was a fool in not noticing that the value is negative because it is bellow y=0. I now, shall have to re-think my entire enquiry.

    Thankyou, mes amis.

    The issue is now resolved.
     
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