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.`

Answer

`((20-12sqrt(2))/(3))` sq units

Explanation

The points in the graph are
`A(1,1), B(sqrt(2),0), C(2,2), D(sqrt(2), 2)`

`therefore ` Required area
`=int_(1)^(sqrt(2)){x^(2)-(2-x^(2))}dx+int_(sqrt(2))^(2){2-(x^(2)-2)}dx`
`=int_(1)^(sqrt(2))(2x^(2)-2)dx+int_(sqrt(2))^(2) (4-x^(2))dx`
`=[(2x^(3))/(3)-2x]_(1)^(sqrt(2))+[4x-(x^(3))/(3)]_(sqrt(2))^(2)`
`=[(4sqrt(2))/(3)-2sqrt(2)-(2)/(3)+2]+[8-(8)/(3)-4sqrt(2)+(2sqrt(2))/(3)]`
`=((20-12sqrt(2))/(3))` sq units