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Area bounded by curves

  1. Feb 9, 2014 #1
    Hello,

    quick question really.

    1. The problem statement, all variables and given/known data

    Find the area bound by the x axis, [itex]x = 1[/itex], [itex]x = 4[/itex] and [itex]y = 2/x[/itex]

    2. Relevant equations



    3. The attempt at a solution

    Representing this graphically, the question is equivalent to performing the definite integral of [itex]y = 2/x[/itex] from [itex]1[/itex] to [itex]4[/itex]. Right?

    Which would result in the area being equal to [itex]2 ln(4)[/itex]

    It seems painfully obvious but this question has made me doubt myself so I wanted to check I haven't missed anything obvious... i.e is there any reason to do the longhand of subtracting the smaller areas from the larger ones.

    Thanks,

    BOAS
     
  2. jcsd
  3. Feb 9, 2014 #2
    You are absolutely correct. I see no reason to put anything more than the integral you described. For any positive, integrable function, the area between the curve and the x-axis is equal to the definite integral of the function over the region concerned.
     
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