00:01
So let us start with the concept which we are going to use here for this question.
00:07
So area between a curve can be given as integral a to b mod over f of x minus of g of x dx.
00:18
So this is what representing area between the curves.
00:21
So we are given the two curves.
00:23
First one is y square is equals to x.
00:25
Second one is y is equals to x minus of 2.
00:28
If you will try to draw this curves on the graph.
00:32
So let's say this is the x axis, this is y axis.
00:36
On putting x as 0, y will be minus 2.
00:39
On putting x as 1, y will be minus 1.
00:44
That means the line is something a straight line passing from this minus of 2 point.
00:51
And similarly way y square is equals to 0.
00:54
It's nothing but an hyperbola at origin.
00:58
So according to this, you have to find the area bounded between this curve.
01:06
So let's get started with this.
01:08
So first of all, we need to find the critical points or the limits for x.
01:13
For that y square is equals to x.
01:16
This can be written as y is equals to under root of x.
01:21
And already we have given y is equals to x minus of 2.
01:26
Let's take 2 to that side.
01:28
X will be equals to y plus 2.
01:32
Equating both of them.
01:33
Sorry.
01:34
So equating both of them, we get under root of x is equals to x minus of 2.
01:41
Taking under root of x to that side will become x minus under root of x minus of 2.
01:47
This should be equals to 0.
01:50
This can be written as under root of x that whole square minus under root of x minus 2 is equals to 0.
01:56
I can make the roots like i want minus 2 and minus 1.
02:00
So 2 and z are 2 for minus.
02:04
It should be negative here.
02:06
So we can make the root like under root of x minus 2 and under root of x plus 1 is equals to 0...