Is inutaisho really dead? or is he still alive somewhere?

i know that in a early episode of inuyasha we saw a body of a great demon. but was that really inuyasha's father? i don't think it was.i know in the 3rd movie we saw him die in the begining of the movie and reapper as a ghost.but it could have been a astral form of him that we saw, what do you guys think