00:01
So again, we need to find the, we need to draw the curves, given curves.
00:08
And this time, it's not very clear the function is it can be represented by x or y.
00:20
So we reform this first formula here.
00:24
And we can see that we can express x in terms of y very easily.
00:31
We just move y squared to the other side and divided by 4.
00:35
So it will be 12 minus y square over 4.
00:46
And this is just x equals y.
00:52
After reformulating, we can see that we can say everything is represented by y.
00:59
So why don't we take the integrate with respect to y? then let's draw the pictures.
01:09
Here is xxy axis.
01:14
If i draw this, this is a problem.
01:19
When y equal to 0, x equal to 3.
01:23
So, let's look like this.
01:29
And when x equals to 0, y equals to 12.
01:35
So y will um, uh, y square will equals 12.
01:42
So y equals to 2 times square root 3 and negative 2 times square root 3.
01:56
So this problem will look like this.
02:04
And i also got this y equals x.
02:08
It's a straight line.
02:12
And then we've got those two intersections.
02:17
So this is a equals y and if we noted this, denote this intersection x1 here, this intersection is x2 here a corresponding x1 corresponding to y1 and x2 corresponding to y1.
02:57
Since we decide to integrate with respect to y, let's find our y1 and y2.
03:04
Right here is the enclosed region right in order to find the y1 and y2 we know it they should satisfy this equation 12 or minus y square over 4 equals y that's when those two curves intersect right so this will give us some we times 4 on both and move everything to the right.
03:44
It will give us a y square plus 4y minus 12.
03:54
We go to 0.
03:56
And we can solve this by factor.
04:00
By factoring.
04:01
So this is y plus 6 and y minus 2.
04:11
We go to 0...