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[music] Welcome back to Calculus One, and
welcome to Week 10 of our time together.

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Now, for the last few weeks, we've been
looking at applications of the derivative,

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right?
We looked at related rates, at

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optimization problems and most recently,
numerical applications of the derivative.

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This week, in Week 10, we change gears.
We look at anti-differentiation.

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What is anti-differentiation?
Well, it's really the opposite of

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differentiation, right?
When I ask for the derivative of a

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function, right?
I give you a function, you give me a

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derivative.
To anti-differentiate means I give you a

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function, you give me another function
whose derivative is the function I gave

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you, right?
To anti-differentiate means to

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differentiate in reverse, right?
To start with a function and find a new

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function whose derivative is the given
function.

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Now, this turns out to be way harder than
differentiating, right?

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Differentiating is hard because it's, you
know, a technical process and you've got

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to apply the rules carefully.
But there's not a lot of creativity in how

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you apply the derivative rules.
In contrast, anti-differentiating leaves a

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ton of room for creativity and flashes of
insight, which I think will make it a lot

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more fun.
Another question you might have is, why

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we're doing this at all?
Right?

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Why is it worth our time trying to undo
differentiation?

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Anti-differentiation is really a bridge
between two different parts in the course,

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right?
The first 2 3rd of this course has been

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about derivatives and, and the last third
of this course is about something called

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integration.
It turns out that anti-differentiation

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connects differentiation and integration,
which is what we're going to be spending

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the last third of the course doing.
So, maybe it doesn't seem super

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well-motivated right now, but when we get
to something called the Fundamental

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Theorem of Calculus, all this
anti-differentiation stuff is really going

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to crystallize.
This week, we're really just focusing on

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the mechanics of how to undo
differentiation.

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I hope you have fun.
If you're confused or, or really excited

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about how things are going in the course,
really however you're feeling, post

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something to the forums, right?
All of us on the teaching staff want to

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hear from you.
Good luck.