LC circuit impulse response
It appears  to me that you were given a 1A DC current source at t=0 ( but did't tell us) and LC oscillates with a 4 second cycle. Then an impulse is applied at 9s.
I get ΔV=54.9758 (2/π/11.58mF) which give a net result of -1mV.
But I would call it zero.
It is a 4 second LC cycle so t=9s is the same as t=1s, 5s.