Sign of integral and limits...

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  1. sabre2th1's Avatar
    1 20-06-2012  13:13
    • Exalted and Worshipped Member
    • Location: Southampton
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    Sign of integral and limits...


    I was watching an ExamsSolutions video on Youtube, and the guy who does them done the above.. He said if you change the sign of the integral the limits switch.. Now my question is, say if there was no -64 at the start of the above integral. If you wanted to switch limits, you would essentially multiply the integral by -1?
  2. Zuzuzu's Avatar
    2 20-06-2012  13:23
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    Re: Sign of integral and limits...
    Yes.

    If \displaystyle \int_{a}^{b} f(x) \mathrm{d} x = F(b) - F(a), then \displaystyle - \int_{a}^{b} f(x) \mathrm{d} x = - (F(b) - F(a)) = F(a) - F(b) = \int_{b}^{a} f(x) \mathrm{d} x.
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  3. sabre2th1's Avatar
    3 20-06-2012  13:27
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    Re: Sign of integral and limits...
    (Original post by Zuzuzu)
    Yes.

    If \displaystyle \int_{a}^{b} f(x) \mathrm{d} x = F(b) - F(a), then \displaystyle - \int_{a}^{b} f(x) \mathrm{d} x = - (F(b) - F(a)) = F(a) - F(b) = \int_{b}^{a} f(x) \mathrm{d} x.
    Nice way to put it ! Thanks mate !
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