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Finding area with integration and arbitrary line

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Sketch the region bounded by y = x^2 and y = 4. This region is divided into two sub regions of equal area by a line y = c. Find c.

    2. Relevant equations

    3. The attempt at a solution

    I try to integrate from 0 to a point c and make it equate to from integrating c to 4 like this:


    \int_{0}^{c} [(\sqrt{y})-(-\sqrt{y})]dy = \int_{c}^{4} [(\sqrt{y})-(-\sqrt{y})]dy


    But after I simplify the c disappears.. is this wrong?
  2. jcsd
  3. Feb 8, 2010 #2


    Staff: Mentor

    Because of the symmetry of this problem, it suffices to look at the region in the first quadrant only.

    [tex]\int_{0}^{c} \sqrt{y}~dy = \int_{c}^{4} \sqrt{y}~dy [/tex]
    Try working with this equation - c doesn't disappear.
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