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Calculus I: Integrals are Gonna Carry that Weight

Calculus is the branch of mathematics that tells us how to break down mathematical objects and put them back together. Whether you credit Isaac Newton or Gottfried Leibniz with its invention, there’s no denying physics is built upon a foundation of calculus.

We frequently break calculus into two subfields:

  • The derivative calculus, which–like breaking a staircase into individual steps–tells us how to deconstruct wholes into constituents, and
  • The integral calculus, which does the reverse: given an assortment of steps, it manages to build a staircase. 

Today, we introduce the latter topic. We do so in the context of finding the area of a shape in the real plane, and then generalize this procedure to craft our real goal: the integral. The integral is a powerful machine, capable of feats akin to mathematical alchemy.

Are you ready? Okay, 3… 2… 1… Let’s jam!

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