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Math Help - Integration by Substitution question?

  1. #1
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    Integration by Substitution question?

    Can you please show me the steps to integrate:

    ∫(x/2-x) dx ?? i let u = (2-x) and then??

    Help is very appreciated! thanks!!
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  2. #2
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    Quote Originally Posted by Yehia View Post
    Can you please show me the steps to integrate:

    ∫(x/2-x) dx ?? i let u = (2-x) and then??
    Then differentiate u=2-x to get du=-dx, besides x=2-u. Can you take it?
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    Then differentiate u=2-x to get du=-dx, besides x=2-u. Can you take it?
    I do do that! to get: ∫ (u-2)/u du

    and that simplifies to : ∫ 1 - 2u^-1 du

    still stumped though :S
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  4. #4
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    Well done, you almost got it. (Oh, the numerador is actually 2-u.)

    Next step is to note that \int du=u+k and \int\frac{du}u=\ln|u|+m.
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  5. #5
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    Quote Originally Posted by Krizalid View Post
    Well done, you almost got it. (Oh, the numerador is actually 2-u.)

    Next step is to note that \int du=u+k and \int\frac{du}u=\ln|u|+m.

    But the numerator is MINUS x isnt it? and if x = 2 - u, then -x = u - 2 ? if im not wrong?

    And i dont understand your second bit (which is right btw, according to the book) can you explain?

    thanks a lot
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  6. #6
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    Ah yes, you're right, I forgot the minus sign when differentiating.

    The latter are basic formulae which you should know, I can't help you any further about that, so check your notes.
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