Answer :

Given the boundaries of the area to be found are,


• The curve y = 4-x2


• The y-axis


• y = 0 (x - axis)


• y = 3 (a line parallel to x-axis)


Consider the curve,


y = 4-x2


x2 = 4-y


---- (1)



About the area to be found,


• The curve y = 4 - x2, has only the positive numbers as x has even power, so it is about the y-axis equally distributed on both sides.


• From (1) as, , the curve has its vertex at (0,4) and cannot g•beyond y = 4 as the value of x cannot be negative and imaginary.


• y= 0 is the x – axis


• y =3 is parallel to x-axis which is 3 units away from the x-axis.


The four boundaries of the region to be found are,


Point A, where the x-axis and meet i.e.


C(-2,0).


Point B, where the curve and y=3 meet where x is negative.


Point C, where the curve and y=3 meet where x is positive.


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


Area of the required region = Area of ABCD.




[Using the formula]




The Area of the required region


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