Find the area bounded by the curve y=(4-x²), the y-axis and the lines y=0,y=3.

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