Answer :

Given the boundaries of the area to be found are,

• The curve y = x^{3}

• The y= 0, x-axis

• x = 2 (a line parallel toy-axis)

• x = 4 (a line parallel toy-axis)

As per the given boundaries,

• The curve y = x^{3} is a curve with vertex at (0,0).

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

• x=4 is parallel toy-axis at 4 units away from the y-axis.

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

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

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

•Point C, where the x-axis and x=4 meet i.e. C(4,0).

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

Area of the required region = Area of ABCD.

[Using the formula ]

= 60 sq. units

The Area of the required region = 60 sq. units.

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