Find the value of k for the integral

[Emethyst]

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.

[Mark44]

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

By observation, it looks like k will be somewhere around 1/2.

[Emethyst]

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).

[Mark44]

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!