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Incomplete integration explanation

  1. Nov 29, 2013 #1
    hello,

    i have a question about an explanation of integration as finding the area under a curve. I don't have any problems doing the integration but it's more a case of why?

    Finding the area bound by two curves is easy enough but what does that area actually mean?

    I know that it's a useful tool applied to physical examples where the area under the curve of something like radioactive decay has units, but I don't understand what it means to speak of area without giving it some units.

    I hope that makes sense and that I have posted this in a relevant subsection. I don't know if it's a useful question to ask, but if there is an answer out there, I would be interested to know.

    Thanks,

    BOAS
     
  2. jcsd
  3. Nov 29, 2013 #2

    tiny-tim

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    Hi BOAS! :smile:

    Suppose you have a graph of force against time, for when a bat hits a ball.

    The area under the curve is the total momentum imparted to the ball.

    (and it equals ∫ F dt, which comes from F = d(momentum)/dt)
     
  4. Nov 29, 2013 #3
    Hello,

    thanks for the response.

    I do appreciate that integration as a method for finding the area beneath a curve is an extremely useful tool. What is bugging me a little, is the idea of finding the area bound by say, two curves. It doesn't seem meaningful to speak of area without units, although a quick sketch of the curve will tell you that there is indeed an area there.

    It isn't really a big deal, but "area = 4" just feels odd and I was wondering if there was some explanation of why it can make sense without needing any units.
     
  5. Nov 29, 2013 #4

    tiny-tim

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    Hello BOAS! :smile:
    there are units …

    eg in my example, the axes had units of newtons and seconds, with an area of newton-seconds

    (and for an example of what an area-bounded-by-two-curves can represent, see http://en.wikipedia.org/wiki/Hysteresis :wink:)
     
  6. Nov 29, 2013 #5
    I do understand your example - I think i'm splitting hairs really.

    In my maths class we've been doing problems that don't represent any physical thing, so neither axis had units.

    I don't think it's especially important, I was just curious to see if there was a mathematical reason for being able to talk about are without units.
     
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