# Find the value of k for the integral

## 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.

Mark44
Mentor
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.

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
Mentor
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!