I can’t conceptually grasp this the same why I can grasp addition/subtraction (the opposite of adding stuff is to take it away), but if the derivative of a function is the slope at any given point, then why would the area under the curve be the opposite of that?
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It’s the same as you said about addition and subtraction.
The derivative is a slope, calculated by taking the value of a function, **subtracting** a nearby value and **dividing** by the short horizontal distance between them. The integral is a cumulative area, calculated by **multiplying** a short horizontal distance by the value of the function and **adding** it to the total.
It’s the opposite arithmetic steps, in the opposite order. Everything else, limits and epsilons and all that, is just mathematicians being fancy. 😉
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