Find area of region
Given,
• R = {(x,y): x2 ≤ y ≤ x}
From the set we have the curve, y = x2 ------ (1)
Also the line equation y = x ------ (2)
As per the given boundaries,
• The curve y =x2, has only the positive numbers as x has even power, so it is about the y-axis equally distributed on both sides.
• y = x is a line passing through the origin.
The boundaries of the region to be found are,
•Point A, where the curve y = x2 and y=x meet, i.e. A (1,1)
•Point O, which is the origin
Drop a perpendicular D on the x-axis from A, where D = (1,0)
Now,
Area of the required region = Area of OPAQO.
Area of OPAQ•= Area of OPAD•– Area of OQADO
[Using the formula ]
The Area of the required region