Compute · surfingcomplexity.blog
Asking students to compute the derivative of this function would be a perfectly reasonable question on a Cal 1 final
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But asking students to compute the integral of this function on a Cal 2 final exam would be unfair, because it’s not possible to do with the techniques they learned in class (at least, the reporter didn't learn the technique you’d need until Cal 3).
Key facts
- If you study calculus, you’ll first be taught differential calculus (sometimes referred to “Calculus 1” or “Cal 1”) and then you’ll be taught integral calculus (“Cal 2”)
- You might ask, “how quickly is this curve changing when x=6?” In other words, what is the slope of this function right in a neighborhood close to x=6
- But asking students to compute the integral of this function on a Cal 2 final exam would be unfair, because it’s not possible to do with the techniques they learned in class (at least, the reporter didn't learn
- Back in 2011, somebody asked about this on the Mathematics Stack Exchange: Why is integration so much harder than differentiation
Summary
Over the years, mathematicians, logicians and computer scientists have developed various calculi. If you have a background in computer science, you’ve likely heard of the lambda calculus, a model of computation that was developed by Alonzo Church. Visually, you can think of differential calculus as being about calculating the slope of a function at a given point. You might ask, “how quickly is this curve changing when x=6?” In other words, what is the slope of this function right in a neighborhood close to x=6? Integral calculus, on the other hand, is about the area under the graph over a particular interval. If you study calculus, you’ll first be taught differential calculus (sometimes referred to “Calculus 1” or “Cal 1”) and then you’ll be taught integral calculus (“Cal 2”). When you study differential calculus, you learn the rules for calculating the derivative (slope-at-a-point) of a function.