00:01
All right, we want to graph, we want to find the area bounded by the y axis on the left, the x equals two square roots of y on the right, and then on the upper left, this parabola, and on the upper right, this.
00:27
So i think we don't include this right here, even though that's part of the x, equals the square to 1 minus y squared.
00:37
I can't see your picture that it says to look at.
00:43
So what i'm guessing is they mean this area right here.
00:51
All right, let me take that scribble off.
00:53
Okay, we're going to try and find the area, and it looks like if we cut it up and down, we'll have to do two integrals, one from zero to this point of interstate.
01:10
And then we'll have to do the next one from that point of intersection to this point of intersection.
01:18
All right, so we need to find where the black one, which is x equals 3 minus y, intersects with the red one, which is y minus 1 squared.
01:27
So 3 minus y equals y minus 1 squared.
01:34
3 minus y equals y squared minus 2y plus 1.
01:38
So 0 equals y square minus, let's see, i'm adding y, so minus 1, subtract 3, so minus 2, so y equals 2 or y equals 1.
02:04
Okay, so this will be where y equals 2.
02:15
So at this point, i don't know why didn't write them down when i was running it.
02:18
This is 2 .1.
02:21
All right, now we need to find where the black one intersects with the blue one.
02:25
So 3 minus y equals two square roots of y.
02:32
Okay, i'm going to square both sides here to get that square root out.
02:36
So we get 9 minus 6y plus y squared equals 4 y.
02:42
So y squared, subtract that over there, minus 10y plus 9 equals 0.
02:48
So y minus 1, y minus 9 equals 0.
02:58
So y equals 1 or 9.
03:00
So this looks at like y equals 1.
03:03
And when we plug, oops, y, oh, wow.
03:09
Oh, okay.
03:14
Okay, at this point here was y equals 2, x equals 1.
03:19
So that's name is 1 2...