Answer :

Given the boundaries of the area to be found are,

• The curve

• The x-axis

• x = 0 (y-axis)

• x = 4 (a line parallel toy-axis)

As per the given boundaries,

• The curve,is a curve with vertex at .

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

• x=0 is the y-axis.

• The four boundaries of the region to be found are,

•Point A, where the curve y^{2} = 6x + 4 and x=0 meet.

•Point B, where the curve y^{2} = 6x + 4 and x=2 meet.

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

•Point O, or the origin i.e. O(0,0).

Area of the required region = Area of OABC.

[Using the formula ]

The Area of the required region

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