Results 1 to 2 of 2

Math Help - Two Questions

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    6

    Two Questions

    1. When asked to sketch the region of {(x,y)|x^{2}\le y\le 2}
    I'm pretty sure this is just an oval with it's two halves being x^2 from  -\sqrt{2} to \sqrt{2} but I'm not sure if thats right.
    2. I'm suppose to set up a proper and improper integral to find the length of a curve y^3 = x  from (-1,-1)  to  (8,2).
    I believe I've found the proper one to be \int_{-1}^{2} \sqrt{1+9y^4} dy
    Any hints on what the improper one might be?
    Thanks in advance for the help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    It's not real obvious that you have or have not the first one correctly determined. The way I might do it...

    Graph y = 2

    Graph x^2 = y

    This divides the x-y plane into 5 distinct sections. Just pick a poitn from all 5 and see if it works.

    Above the line and inside the parabola

    (0,3)

    Above the line and right of the parabola

    (3,3)

    Above the line and left of the parabola

    (-3,3)

    Below the line and inside the parabola

    (0,1)

    Below the line and outside the parabola

    (2,1)

    Let's see

    (0,3): o^2 = 0 <= 3 <= 2 -- Nope.
    (3,3): 3^2 = 9 <= 3 -- Nope.
    (-3,3): (-3)^2 = 9 <= 3 -- Nope.
    (0,1): 0^2 = 0 <= 1 <= 2 -- Yes!
    (2,1): 2^2 = 4 <= 1 -- Nope.

    That settles it. Below the line and inside the parabola.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. More log questions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 31st 2010, 04:58 PM
  2. Please someone help me with just 2 questions?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 4th 2009, 04:55 AM
  3. Some Questions !
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 3rd 2009, 03:09 AM
  4. Replies: 4
    Last Post: July 19th 2008, 07:18 PM
  5. Replies: 3
    Last Post: August 1st 2005, 01:53 AM

Search Tags


/mathhelpforum @mathhelpforum