Two curves C_(1)equiv[f(y)]^(2//3)+[f(x)]^(1//3)=0 and C_(2)equiv[f(y)]^(2//3)+[f(x)]^(2//3)=12, satisfying the relation "(x-y)f(x+y)-(x+y)f(x-y)=4xy(x^(2)-y^(2))
The area bounded by C_(1) and x+y+2=0 is

Options

A. `5//2` sq. units
B. `7//2` sq. units
C. `9//2` sq. units
D. None of these

Answer

C

Explanation

`"Required area "=overset(2)underset(-1)int(-y^(2)-(-y-2))dy`
`=[(y^(2))/(2)+2y-(y^(3))/(3)]_(1)^(2)`
`=[(4)/(2)+4-(8)/(3)-((1)/(2)-2+(1)/(3))]`
`=9//2` sq. units.