Find the value of k for the integral

[Emethyst]

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

definite 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.

 

[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!