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Find the area of the region bounded by y = √x and y = x
The given equations are,
And y = x ...(ii)
Solving equation (i) and (ii)
= x = y
Or = y
Or y(y – 1) = 0
So, y = 0 or y = 1 and x = 0 or x = 1
On solving these two equations, we get the points of intersection.
The points are O (0, 0) and A(1,1). These are shown in the graph below
Now the bounded area is the required area to be calculated,
Hence, Bounded Area, A = [Area between the curve (i) and x axis from 0 to 1] - [Area between the curve (ii) and x axis from 0 to 1]
On integrating the above definite integration,
Area of the region bounded by and Y = X is.