for a paper that I need to write for my math class for the IB diploma programme I was interested in modeling the surface area of different kinds of bottles: I initially wanted to use this formula:
Formula:
$$A=2\pi\int_a^bf(x)\sqrt{1+[f’(x)]^2}dx$$
However, I quickly realized that many of my functions that I generated via applying curve fitting on the bottles that I had been planning on applying this formula to (in order to find the surface area of the bottles) were more complex trigonometric functions.The paper I'm writing is very limited in space, and I'm obligated to explain the steps taken thoroughly. This makes me wonder, would it be appropriate to try and approximate these trigonometric functions as polynomials instead because I feel like the formula would be easier to apply to them? Apologies if this seems like a straightforward question, we were not taught anything about Taylor Series in class and it is not in the syllabus for the course I'm taking :p