a.  1.  
1.  Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.  
2.  Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.  
3.  (Math.) Of, pertaining to, or being, a whole number or undivided quantity; not fractional.
 
n.  1.  A whole; an entire thing; a whole number; an individual.  
2.  (Math.) An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.

Noun  1.  integral  the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x) 
Adj.  1.  integral  existing as an essential constituent or characteristic; "the Ptolemaic system with its builtin concept of periodicity"; "a constitutional inability to tell the truth" 
2.  integral  constituting the undiminished entirety; lacking nothing essential especially not damaged; "a local motion keepeth bodies integral" Bacon; "was able to keep the collection entire during his lifetime"; "fought to keep the union intact" 