Some of my professors claim it’s the infinitismal section of the graph, and some say it’s just notation. Then my professor said the differential of a function and the derivative of a function are two different things, whatever that means. I’m just all very confused. Plz help.
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The integral is the area under a function. This can be done by making a lot of rectangles, and taking the sum of the area of each rectangle. (https://en.m.wikipedia.org/wiki/Riemann_sum for some visualisation). The rectangles will have an area of f(x_i) * ∆x, where x_i is a different point on the x-axis (f(x_i) becomes the rectangle’s height), and ∆x is the width of each rectangle.
When the amount of rectangles go to infinity, in order to get the exact area (the infinite series will converge, this is called a riemann sum), the width ∆x will go to 0. When taking the limit as ∆x goes to zero, ∆x becomes dx (this is notation). We also change the notation from being a sum (large sigma) to the integration sign you’re probably familiar with. Thus, the dx is sort of a remnant of the infinite series.
It also tells you which variable to integrate, which is nice.
This is at least how I think of it.
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