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[MUSIC]. 

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Welcome back to Calculus One. 
And welcome back to Week 14 of our time 

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together. 
This is the panultimate week. 

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Next week is Week 15 and that's it, 
right, there's 15 weeks in this course 

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altogether. 
Now at this point, we've got the 

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fundamental theorem of Calculus which 
produces integration to 

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antidifferentiation. 
And last week, we looked at 

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U-substitution. 
U-substitution was a technique that made 

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it possible for us to figure out how to 
use the Chain Rule in reverse to do a ton 

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more antidifferentiation problems. 
This week, in Week 14, we continue 

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techniques of integration. 
In particular, we're going to look at 

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integration by parts which is really the 
product rule in reverse. 

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Just like U-substitution is the Chain 
Rule in reverse, parts is just the 

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Product Rule in reverse. 
And the Product Rule came up fairly 

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frequently so knowing how to reverse it 
is going to let us do a ton more 

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integration problems. 
Next week, in Week 15, we're going to 

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look at some more applications of 
integration, really focusing on volume 

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calculations, which I think are a lot of 
fun because it will give us a chance to 

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think 3-dimensionally. 
And then, we've got the final exam and 

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that's it. 
So, hang in there, we've just got one 

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more week after this and then it's the 
end of the course. 

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We're going to make it.