Integration Taught Correctly

[Math the World] claims that your calculus teacher taught you integration wrong. That’s assuming, of course, you learned integration at all, and if you haven’t forgotten it. The premise is that most people think of performing an integral as finding the area under a curve or as the “antiderivative.” However, fewer people think of integration as adding up many small parts. The video asserts that studies show that students who don’t understand the third definition have difficulty applying integration to real-world problems.

We aren’t sure that’s true. People who write software have probably looked at numerical integration like Simpson’s rule or the midpoint rule. That makes it pretty obvious that integration is summing up small bits of something. However, you usually learn that very early, so you’re forgiven if you didn’t get the significance of it at the time.

Even if you didn’t learn calculus, the video is an easy introduction to the idea of integration with practical examples drawn from basketball, archery, and more. Although there is a bit of calculus terminology, the actual problems could just as easily have been the voltage on a charging capacitor, for example.

We think calculus has a bad rap as being difficult when it isn’t. Maybe you should take more than 20 minutes to learn it.

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