( t + 1+ t ^2 ) 1+ t ^2 dt = 1 2 [ ~g ( t )]^2+ c , (where c is a constant of integration) then g(2) is

Step-by-step solution

Put ( t + 1+ t ^2 )=y aligned & [ 1 t + 1+ t ^2 (1+ t 1+ t ^2 ) ] dt = d y & 1 1+ t ^2 dt = d y aligned aligned ( t + 1+ t ^2 ) 1+ t ^2 dt & = y ~d y & = y^2 2 + c & = [ ( t + 1+ t ^2 ) ]^2 2 + c aligned aligned & g(t)= (t+ 1+t^2 ) & g(2)= (2+ 1+2^2 )= (2+ 5 ) aligned