Normally, calculus is an advanced high school or even university subject. However, with only understanding of basic linear equations, the intuition behind calculus can be grasped without any confusing mathematical concepts.
Suppose you own a lemonade stand, and you want to keep track of how much you sell each day. Under this arbitrary hypothetical scenario, each day you have the same amount of lemonade sold; from this information, you can construct a graph.
Of course, this is not a particularly useful graph, but it’s good enough for our purposes. However, in order to use this graph mathematically, we have to convert this column chart into a line on the xy plane. If you haven’t figured out the relationship representing this graph, it’s y=2.
This is important: we have just created a line to represent our situation, and this enables us to perform calculus.
Now let’s find out how many lemonades you have sold in total up to a given day. This is fairly simple: you just add up all the lemonades sold before and on that day. I will do the math for you, and this is the new column chart. Likewise, I have converted it into a line on the xy plane (The equation for this line is y=2x).
If you look closely at our new line, you will discover that the y-value of the line on a certain day is exactly the amount of lemonades sold up to that day. For example, up to day 2, the graph informs you that you have sold 4 lemonades.
Congratulations! You have just completed integration, one of the 2 fundamental processes in calculus. Loosely speaking, integration is finding the area underneath a line. Here, the line y=2x is what we get after the integration, and the earlier line y=2 is what we integrated from, because we have calculated the area between the line y=2 and the x-axis and recorded this area in our graph of y=2x. This has gotten us the result we wanted: the total amount of lemonades sold up to each day.
In part 2, we are going to explore the other fundamental process of calculus: derivation.
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