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Question

The area of the region bounded by parabola y2 = x and θ the straight line 2y = x is
(a) 43sq. units (b) 1 sq. units (c) 23sq. units (d) 13sq. units

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Solution

To find: area of the region bounded by parabola y2 = x and the straight line 2y = x

y2 = x ..(1)
2y = x ..(2)

Solving (1) and (2), we find the coordinates of the point of intersection A.
i.e., A(4, 2)



The area of the shaded region OAO = (Area of the upper curve − Area of the lower curve)
Thus,
Required area=04xdx-04x2dx =x323204-x2404 =23x3204-14x204 =23432-032-1442-02 =2323-1416 =163-4 =16-123 =43Thus, Area=43 sq. units

Hence, the correct option is (a).

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