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Find the value of k for the integral

  1. May 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the value of k so that the region enclosed by f(x)=sqrt(x+2), the x-axis, and the line x=2 is divided by x = k into two regions of equal area.



    2. Relevant equations
    definate integral properities, fundamental theorem of calculus



    3. The attempt at a solution
    I have no problem finding the integral for this area, i'm just confused over the last part of the question and the use of the line x = k. How am I supposed to bring this into the answer to find the value of k that makes the area two equal regions? I had an idea to sub k in for x, but this doesn't appear to be anywhere near the right method. Any help with this question would be greatly appreciated, thanks in advance.
     
  2. jcsd
  3. May 18, 2009 #2

    Mark44

    Staff: Mentor

    You want to find k so that
    [tex]\int_{-2}^k \sqrt{x + 2} dx = \int_k^2 \sqrt{x + 2}dx[/tex]

    By observation, it looks like k will be somewhere around 1/2.
     
  4. May 18, 2009 #3
    Ahh thanks for that Mark, I see how to do it now, and the answer is actually a weird decimal that in exact form is 2(cuberoot2 - 1).
     
  5. May 18, 2009 #4

    Mark44

    Staff: Mentor

    Which to two decimal places is .52, so my guess was pretty close!
     
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