1.

"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

Answer»

`5//2` sq. units
`7//2` sq. units
`9//2` sq. units
None of these

Solution :
`"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.


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