The region is bounded by the parabola x2=y (opening upward, vertex at origin) and the horizontal line y=4, in the first quadrant where x≥0 and y≥0.
Setting y=4 in x2=y:
x2=4
x=2 (first quadrant)
The curves meet at (2,4).
In the region from x=0 to x=2:
Top curve: y=4
Bottom curve: y=x2
A=∫02(4−x2)dx
A=[4x−3x3]02
=(4(2)−3(2)3)−(0−0)
=8−38
=324−8
=316
The area of the region =316 square units.