If (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 equal to

Step-by-step solution

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