He's correct for .

He used 25 instead of 16.



The differential of volume is a thin square slab,
(think of a thin square linoleum floor tile) whose
thickness is dx thick. Think of the green slab being
a square (I know it doesn't look like a square, but
pretend it is a square whose edge is on the thin black
strip and imagine it sticking straight up out of the 
paper straight up toward you, perpendicular to the 
xy-plane, not slanted as it looks like here.)

The length of the edge of the slab is 

 =  =

The vertical height of the slab is the same, since it's square,
and its thickness is dx, so the differential of volume is

 or 

The slabs go from where x=-4 to +4

So

 =  =  

Finish that by breaking it into two integrals and you'll
end up with .

Edwin