Answer :

Given the boundaries of the area to be found are,


• The curve y = x3


• 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 = x3 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 = x3 and x=2 meet.


Point B, where the curve y = x3 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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