Find the area of the region bounded by the curves `y=x^2,y=|2-x^2|,a n dy l=2,` which lies to the right of the line `x=1.`

Options

A. `((12-20sqrt(3))/(2))` sq. units
B. `((20-sqrt(2))/(3))` sq. units
C. `((20-12sqrt(2))/(3))` sq. units
D. `((12-20sqrt(2))/(3))` sq. units

Answer

c

Explanation

Let A be the required area. Then,
A = Area ABCA + Area BCD
`implies A =underset(1)overset(sqrt(2))int{x^(2)-(2-x^(2))}dx + underset(sqrt(2))overset(2)int {2-(x^(2)-2)}dx`
`implies Aunderset(1)overset(sqrt(2))int (2x^(2)-2)dx + underset(sqrt(2))overset(2)int(4-x^(2))dx`
`implies A =[(2)/(3)x^(3)-2x]_(1)^(sqrt(2))+[4x-(x^(3))/(3)]_(sqrt(2))^(2)=((20-12sqrt(2))/(3))`sq. units.