Nothing. Integram has no relevance to calculus.
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In the ancient system of Greek numbers it had the value 5. In calculus it is often used to represent very small values.
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.