, area bounded by parabolas
y2 = 4x and x2 = 4y divides the area of the square in three equal parts Example 14 Find the area of the region
{(x, y) : 0 ≤ y ≤ x2 + 1, 0 ≤ y ≤ x + 1, 0 ≤ x ≤ 2}
Solution Let us first sketch the region whose area is to
be found out This region is the intersection of the
following regions A1 = {(x, y) : 0 ≤ y ≤ x2 + 1},
A2 = {(x, y) : 0 ≤ y ≤ x + 1}
and
A3 = {(x, y) : 0 ≤ x ≤ 2}
The points of intersection of y = x2 + 1 and y = x + 1 are points P(0, 1) and Q(1, 2)