Answer :

To find region enclosed by


y2 = x ...(i)


And x + y = 2 ...(ii)


From equation (i) and (ii),


y2 + y – 2 = 0


Or, (y + 2) (y – 1) = 0


Or, y = – 2, 1


x = 4,1


Equation represents a parabola with vertex at origin and its axis as x - axis


Equation represents a line passing through (2,0) and (0,2)


On solving these two equations, we get point of intersections. The points of intersection of line and parabola are (1,1) and (4, – 2) These are shown in the graph below



Shaded region represents the required area. We slice it in rectangles of width Δy and length = (x1 – x2).


Area of rectangle = (x1 – x2)Δy.


Required area of Region AOBA









The area of the region included between the parabola y2 = x and the line x + y = 2.


is


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