Q24 of 45 Page 1

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

Given: equation of parabola and line are respectively


Y2 = x ⇒ y = √x … (1)


X + y = 2 ⇒ y = 2 – x … (2)


From (1) and (2), we get


⇒ (2 – x)2 = x


⇒ 4 + x2 – 4x = x


⇒ x2 – 5x + 4 = 0


⇒ (x – 4) (x – 1) = 0


∴ x = 1, 4



Area of the bounded region OABCDO = area of region OAE + area of region AEB + area of region OBCDO


= A1 + A2 + A3









∴ Required bounded area


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