Answer :

Given the boundaries of the area to be found are,

• The parabola y^{2} = 4x

• x = 3 (a line parallel toy-axis)

As per the given boundaries,

• The curve y^{2} =4x with vertex at (0,0), has only the positive numbers as y has even power, so it is about the x-axis equally distributed on both sides.

• x= 3 are parallel toy-axis at 3 units from the y-axis.

• The boundaries of the region to be found are,

•Point A, where the curve y^{2} = 4x and x=3 meet when y is positive.

•Point B, where the curve y^{2} = 4x and x=3 meet when y is negative.

•Point C, where the x-axis and x=3 meet i.e. C(3,0).

•Point O, the origin.

Area of the required region = Area of OAB

Area of OAB = Area of OAC + Area of OBC.

[area under OAC = area under OBC as the curve y^{2} = 4x is symmetric]

Area of OAB = 2 × Area of OAC

[Using the formula ]

The Area of the required region

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