Because calculus applications are almost infinite. In fact, every branch of science uses calculus : physics, chemistry, Biology, social studies, economics, etc. Calculus is a universal language that can be used to answer bunches of questions. Using calculus, you can solve various problems including the acceleration of planets in orbit, the kinetic energy of a car in motion, the equivalence point of a chemical reaction, the maximal profit a business can make, the lenght of any curved figure or the area and volume of eccentrical shapes, the electric field produced by a charged object, ... Calculus is interesting because you can use it everywhere!
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Calculus is interesting because it is incredible that human intelligence has discovered a way to solve a problem using a formula that can be repeated. Calculus is not necessarily about the numbers, but about the fact that we can apply rules and theories to numbers in a variety of situations.
Get a good teacher who understands calculus and understands how to teach students in an interesting way (just like I had 50 years ago).
Pre-calculus is supposed to be a stringent review of trig and algebra in preparation for calculus. So, pre-calculus, I would say.
Im still taking Integral Calculus now, but for me, if you dont know Differential Calculus you will not know Integral Calculus, because Integral Calculus need Differential. So, as an answer to that question, ITS FAIR
In short, no. Elementary calculus includes finding limits, basic differentiation and integration, dealing with sequences and series, and simple vector operations, among other concepts. Pre-calculus mostly focuses on the algebra necessary to perform those operations, with perhaps some introduction to limits or other simple ideas from elementary calculus.