If d ^2 ( 2 + 2 ) = +2 |f( )|+c where C is a constant of integration, then the ordered pair ( , f( )) is equal to

Step-by-step solution

aligned & d ^2 ( 2 + 2 ) = ^2 d 2 +1 2 & = ( ^2 - ^2 ) ^2 d 2 + ^2 + ^2 & = ( + )( - ) ^2 d ( + )^2 & = - + ^2 d aligned aligned & = 1- 1+ ^2 d [dividing N ^ r = and ^ r by ] & = 1-t 1+t d t [let =t ] & = (-1+ 2 1+t ) d t & =-t+2 |1+t|+C & =- +2 |1+ |+C & Comparing we get =-1 and f( )=1+ aligned