00:01
So we want to find the area of the region given to us.
00:04
It's very helpful if we graph this because we see that the first region, we have the graph x equals 2 root y.
00:16
And then we see it stops here at 2 -1.
00:22
So this right here is region 1.
00:26
And then region 2, we see there's going to be these two graphs to it.
00:31
There's going to be this one right here, which is x equals y minus one squared.
00:40
And then there's this one right here, which is x equals three minus y.
00:46
So this is the second region.
00:50
What we can do to find these areas is we obviously want to find the area of region one and the area of region two.
00:58
So we're going to start with region one, and we see that for our integration, it's going to be a double integral.
01:07
With regards to y, because we're going to go like this, a horizontal, we're just going to go from zero to one.
01:15
With regards to x, it's going to be from zero to two root y because that's this distance that we're trying to get.
01:24
So then we just have dx, d y, and this gives us integral from zero to y of two root y, d y, taking the integral and applying our limits, we get one -third as the area of region one.
01:40
For region two, it's also going to be a double integral...