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What exactly constitutes as an exact value?

  1. Mar 21, 2013 #1
    I'm not sure if this is the correct section to post in, but since it relates to calculus and this is more of a general concept than a single problem I figured here would be fine.

    On a recent exam we were given a region bounded by a simple curve generated from a function that was bounded from the y-axis to a constant. We were asked to find the exact perimeter of the region. Solving the problem involved solving for the curve and the other two linear sides. Now for the curve I understand you do the integral of the square root of the derivative plus one. I did that, but when I evaluated on the calculator it came out to a very long irrational number. I felt that including a certain number of decimals would be an approximation, not an exact number. So I left it as the value of the other two sides plus the integral. The answer they wanted was anything with at least three decimals. I was not given points as my teacher felt that I did not properly evaluate the problem. Who is the right here?
    Sorry if I'm being vague. We are asked not to post the problems/solutions so I was doing my best to be clear without actually giving the problem.
    Last edited: Mar 21, 2013
  2. jcsd
  3. Mar 21, 2013 #2


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    My guess: there is a closed form expression (what you put into the calcuator) and that is what was asked for.
  4. Mar 22, 2013 #3


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    If you were give [itex]x^2+ y^2= 4[/itex] and asked to find the circumference, "[itex]4\pi[/itex] would be an "exact" answer. "12.566370614359172953850573533118" would not be.
  5. Mar 25, 2013 #4
    Okay, thank you to both of you. The answer could not be written out, so I still think I was correct in the notation I used. That being said, I don't make the decisions so I'll just have to live with things.
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