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Math Help - Definite integral question

  1. #1
    Newbie Nick744's Avatar
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    Definite integral question

    Hey,

    This is the question I can't get out!

    For reference, the answer is 0.0126

    Heres the question: Evaluate.

    Definite integral question-integral1.jpg

    Thanks in advance,
    Nick
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Nick744 View Post
    Hey,

    This is the question I can't get out!

    For reference, the answer is 0.0126

    Heres the question: Evaluate.

    Click image for larger version. 

Name:	integral1.JPG 
Views:	31 
Size:	2.6 KB 
ID:	1705

    Thanks in advance,
    Nick
    The integrand simplifies to 1/(3x^3) + 1/(3x^4) + 1/x^5, so the integral of this is -1/(6x^2) - 1/(9x^3) - 1/(4x^4). Putting in the limits gives:
    [-1/(6*4^2) - 1/(9*4^3) - 1/(4*4^4)] - [-1/(6*3^2) - 1/(9*3^3) - 1/(4*3^4)] = 3133/248832 ( = 0.012591)

    -Dan
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  3. #3
    Newbie Nick744's Avatar
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    Thanks heaps topsquark!

    I have one question though, for the integration I don't understand why the power decreases instead of increase. It may be something we haven't learnt yet as we are into the 3rd exercise of the integration chapter.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Nick744 View Post
    Thanks heaps topsquark!

    I have one question though, for the integration I don't understand why the power decreases instead of increase. It may be something we haven't learnt yet as we are into the 3rd exercise of the integration chapter.
    (Chuckles) But the power DOES increase. -2 > -3 for example. The power rule still applies even though the exponent is negative:
    Int(1/x^n dx) = Int(x^{-n} dx ) = [1/(-n + 1)]*x^{-n + 1} + C

    -Dan
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  5. #5
    Newbie Nick744's Avatar
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    Sorry, I don't know what I was thinking...stupid.

    Please make out like this thread never existed.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Nick744 View Post
    Sorry, I don't know what I was thinking...stupid.

    Please make out like this thread never existed.
    Don't think of it as "stupid." You are now more aware of this property, so your mistake had a use. It is better to ask the question than to not ask it.

    -Dan
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