Question
Find the area bounded by the curve y = x2 and the line y = x.
OR
Find the area of the region {(x. y): x2 ≤ y ≤ x}.
Solution
The given region is {(x, y): x2 ≤ y ≤ x}
This region is the intersection of the following regions:
Consider the equations
...(1)
and y = x ...(2)
From (1) and (2), we get
∴ from (2), y = 0, 1
∴ curves (1) and (2) intersect in the points O (0, 0) and A (1, 1)
Required area = area of the shaded region
This region is the intersection of the following regions:
Consider the equations
...(1)and y = x ...(2)
From (1) and (2), we get
∴ from (2), y = 0, 1
∴ curves (1) and (2) intersect in the points O (0, 0) and A (1, 1)
Required area = area of the shaded region
