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I Determining the limits of x

  1. Dec 11, 2016 #1
    I am currently practicing questions on Green's Theorem however in some questions I have been given a finite region enclosed between a parabola and a horizontal line.

    In these questions I am given 2 values of y but none of x.
    In one question I was given that y = x^2 and y = 9 and was immediately able to spot that x satisfies this for the values -3 and 3 therefore x [-3,3] and y [ x^2, 9]

    However I now have come across a situation where y = 3x^2 and y = 5 and I cannot seem to spot any sort of relationship between these 2. Based on previous questions I figured these values of x would satisfy both values of y given.

    Can anybody tell me how these limits are established? I've integrated in terms of y and now have all x terms but do not know what limits to apply to the integral.
  2. jcsd
  3. Dec 11, 2016 #2
    You can do in exactly the same way:
    $$y=3x^2$$, divide by 3 on both sides to get
    $$y/3=x^2$$, and use the same method as for ##y=x^2##. I would also recommend a figure, in order to see more clearly the region.
  4. Dec 11, 2016 #3


    Staff: Mentor

    What does "y [x^2, 9]" mean?
    It would be much simpler and clearer to say that if x = 3 or x = -3, then y = 9.
    It seems odd to me that you are working with Green's Theorem, but are having trouble solving very elementary equations such as ##3x^2 = 5##. Some time spent reviewing elementary algebra would be very beneficial.
  5. Dec 11, 2016 #4

    Sorry that should have said the limits of y are x^2 and 9 so when we integrate with respect to y those are the limits. It was a poorly written post.

    That is embarrassing, I totally overlooked the other value of y despite specifying it. Brain fart. Thanks for the help!
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