Calculus has been beneficent in nearly all areas of human life and has provided the world with numerous technological advancements such as the ability to measure the area of a piece of property without having to manually do so (e.g., instead of building and measuring a pool to find its area, all we must do is calculate an estimate using calculus).
It provides us an exact method to find the rate of change of a function, allows us to easily prove theories and formulas, and allows us to calculate volumes, optimums, profits, and much more by using only functions and graphs.
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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.
Speaking as someone who is in the engineering field i can tell you that calculus serves no purpose at all for me. Everything is just done with a calculator or a computer so it's all just a bunch of hogwash they put you through for Engineering school that you will never use in the real world unless you are to become a program writer or work in physics.
It is certainly used in calculus, just as calculus can be used in trigonometry.
Calculus is the correct spelling.