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
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.
•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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