00:01
Okay, let's sketch the region.
00:03
The first function is a standard problem.
00:06
So it just looked like this.
00:09
It's open up.
00:13
So this is our y equals to x square.
00:19
Our second function also a problem and we can find when y equal to 0, x either equals to 4 or 0.
00:29
So it crossed the region and 4 0.
00:35
This is our x -axis and this is our y -axis.
00:41
Since the coefficient of x -square is negative, we know it opened downward.
00:50
So this problem is something like this.
00:57
Okay, so this is our y equals to 4x minus x square.
01:09
And the enclosed region is right there by those two problem.
01:15
So we need to find those two intersection points.
01:19
Now we already know they both crossed the region, so we got one.
01:24
So what about the other one? to get the other one, we said this point satisfy both functions.
01:33
So you know x squared equals y equals to 4x minus x squared.
01:40
So we know x square of this point.
01:44
X x2 right we denote this point as x2 so x2 square should equals to y2 and y2 equals to 4x2 minus x2 square and we can get our x2 from here our x2 will be um since x2 is not zero we can cancel with 1 x2 or x2 equals 2.
02:21
Okay.
02:24
Now let's try to evaluate this area...