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Math Help - Why isn't the integral counted twice?

  1. #1
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    Why isn't the integral counted twice?

    Why isn't the integral counted twice?-screen-shot-2012-11-26-11.01.17-am.png

    in the above example when it says that you can add the integral from -2 to -5 TO the integral from -2 to -3, would it not double count the area between -2 and -3?

    similar to an intersection of sets when you have A union B you have to minus A intersect B to get the correct area. Why does that idea not pertain to integrals? Or does it?
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  2. #2
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    Re: Why isn't the integral counted twice?

    Ignore the middle term in the answer. The area from -5 to -3 is (the area from -5 to -2 ) - (area from -3 to -2). There is no ambiguity here.
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    Re: Why isn't the integral counted twice?

    Quote Originally Posted by kingsolomonsgrave View Post
    Click image for larger version. 

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    in the above example when it says that you can add the integral from -2 to -5 TO the integral from -2 to -3, would it not double count the area between -2 and -3?
    \int_{ - 5}^{ - 2} {f}  = \int_{ - 5}^{ - 3} {f}  + \int_{ - 3}^{ - 2} {f}
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