Question

Find approx area of the region between curves y = x^2, y = |2-x^2| and y = 2 which lies right of the line x = 1.

a)" "1/2

b)" "1

c)" "3/2

d)" "None

Solution

The given curves y = x^2, y = |2-x^2| and y = 2 can be traced on x-y cordinate as:

We need to find the area between the curves right of line x = 1.

Area = int_sqrt2\^2 2dx + int_1\^sqrt2 [x^2 - (2-x^2)]dx - int_sqrt2\^2 (x^2 - 2)dx

=> Area = 2(2-sqrt2) + [(x^3)/3 - 2x + (x^3)/3]_1\^sqrt2 + [2x - (x^3)/3]_sqrt2\^2

= 4 - 2sqrt2 + (4sqrt2)/3 - 2/3 - 2sqrt2 + 2 + 4/3 - (4sqrt2)/3

= 20/3 - 4sqrt2

= (20-17)/3

= 1