>>13971201Anon if you are learning calculus for the first time, understanding the derivative as the "rate of change" for the entire starting function, and understanding the integral as the "area under the curve" of a starting function will work just fine. However, you need to internalize the fact that these understandings of the derivative and integral have their limits, as they don't capture the full scope of what those two operations truly are.
When you study Analysis, you will see that the Calculus I definitions of the integral and derivatives fall apart easily in edge cases, and will have trouble generalizing to higher dimensions. Hence, we have the development of Lebesgue integration, or understanding derivatives of multivariable functions in terms of a rank n+1 tensor. Don't miss the forest for the trees anon, and learn your calculus before thinking too hard about it.
