00:01
Hi, in this question, we have been given different curves that are y equal to 2 tender x, then we have y equal to 2x minus 15 and then y equal to 0 and we need to find the area bounded by these regions.
00:21
So let's draw a xy plane and then we will draw the equation curve on this plane.
00:30
So first one is y equal to square root of x.
00:32
So the curve will be parabolic in nature and then second is y equal to 2x minus 15.
00:39
So this will be a straight line having negative slope and let us consider this is y, this is x, then this line that is x axis will be y equal to 0.
00:52
So here we can write this is y equal to 2x minus 15 and this curve is y equal to root under x and this line is y equal to 0.
01:02
So this common region is this denoted by arrow and we need to find the area of this.
01:11
So first of all, we will find this intersection point.
01:14
Let us take this as p.
01:16
So we can write y square equal to x and from here we can write y equal to 2x minus 15.
01:26
So x will be equal to y plus 15 divided by 2.
01:33
So let's put x value here.
01:35
So this will be y square equal to y plus 15 by 2.
01:43
So here we can write 2y square equal to y plus 15.
01:50
So at y equal to 3, if we put here, so this will be 2 times 3 square equal to 3 plus 15.
01:58
So this is 18 equal to 18.
02:00
So y equal to 3 satisfy this condition.
02:02
Also this is in first quadrant so the value will be positive.
02:06
So y coordinate will be 3 then x coordinate will be.
02:09
So we can write since y square equal to x therefore x will be equal to 9...