it's tricky
Well, that question is far too difficult to answer; you should take some Calc courses.
Calculus is the study of the rate at which something changes, in relation to something else... Think slope... except it gets complicated.
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Calculus; by a long shot.
Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
It is certainly used in calculus, just as calculus can be used in trigonometry.
No. Calculus if a field of mathematics.
Calculus is the correct spelling.