integrate vs mathematics

integrate is not a noun while mathematics is a noun.

Word	Noun	Adjective	Verb	Adverb
integrate	No	No	Yes	No
mathematics	Yes	No	No	No

integrate (noun)	mathematics (noun)
	a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

integrate (verb)	mathematics (verb)
make into a whole or make part of a whole
become one; become integrated
calculate the integral of; calculate by integration
open (a place) to members of all races and ethnic groups