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Find the value of k for the integral

  • Thread starter Emethyst
  • Start date
  • #1
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Homework Statement


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.



Homework Equations


definate integral properities, fundamental theorem of calculus



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.
 

Answers and Replies

  • #2
33,152
4,838
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.
 
  • #3
118
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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).
 
  • #4
33,152
4,838
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).
Which to two decimal places is .52, so my guess was pretty close!
 

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