Answer :

Given the boundaries of the area to be found are,


• The parabola y2 = 4x


• x = 3 (a line parallel toy-axis)



As per the given boundaries,


• The curve y2 =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 y2 = 4x and x=3 meet when y is positive.


Point B, where the curve y2 = 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 y2 = 4x is symmetric]


Area of OAB = 2 × Area of OAC




[Using the formula ]



The Area of the required region


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