Answer :

Given the boundaries of the area to be found are,


• The parabola y2 = 8x


• x = 2 (a line parallel toy-axis)



As per the given boundaries,


• The curve y2 =8x, has only the positive numbers as y has even power, so it is about the x-axis equally distributed on both sides as the vertex is at (0,0).


• x= 2 is parallel toy-axis which is 2 units away from the y-axis.


The boundaries of the region to be found are,


Point A, where the curve y2 = 8x and x=2 meet which has positive y.


Point B, where the curve y2 = 8x and x=2 meet which has negative y.


Point C, where the x-axis and x=2 meet i.e. C(2,0).


Area of the required region = Area under OACB.


But,


Area under OACB = Area under OAC + Area under OBC


This can also be written as,


Area under OACB = 2 × Area under OAC


[area under OAC = area under OBC as AOB is symmetrical about the x-axis.]




[Using the formula ]




The Area of the required region


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