Essential Understanding 3.1

Essential Understanding 3.1 Students will understand that antidifferentiation is the inverse process of differentiation.

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A quick vocabulary note: I use "antiderivative" and "integral" interchangeably. They might mean something slightly different, but no one really cares. Everyone just uses "integral" anyways, and so shall I.

So, yeah, integrals and derivatives are opposites. There's not much more to say. Here's an example:

Since the derivative of a position function is a velocity function...

...The integral of a velocity function is a position function!

Since the derivative of a velocity function is an acceleration function...

...The integral of an acceleration function is a velocity function!

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Learning Objective 3.1A Students will be able to recognize antiderivatives of basic functions.

Essential Knowledge 3.1A1 Students will know that an antiderivative of a function f is a function g whose derivative is f.

Essential Knowledge 3.1A2 Students will know that differentiation rules provide the foundation for finding antiderivatives.