Answer :

Given the boundaries of the area to be found are,

• The parabola y^{2} = 8x

• x = 2 (a line parallel toy-axis)

As per the given boundaries,

• The curve y^{2} =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 y^{2} = 8x and x=2 meet which has positive y.

•Point B, where the curve y^{2} = 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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