[MUSIC].
Welcome back to Calculus One. And welcome back to Week 14 of our time
together. This is the panultimate week.
Next week is Week 15 and that's it, right, there's 15 weeks in this course
altogether. Now at this point, we've got the
fundamental theorem of Calculus which produces integration to
antidifferentiation. And last week, we looked at
U-substitution. U-substitution was a technique that made
it possible for us to figure out how to use the Chain Rule in reverse to do a ton
more antidifferentiation problems. This week, in Week 14, we continue
techniques of integration. In particular, we're going to look at
integration by parts which is really the product rule in reverse.
Just like U-substitution is the Chain Rule in reverse, parts is just the
Product Rule in reverse. And the Product Rule came up fairly
frequently so knowing how to reverse it is going to let us do a ton more
integration problems. Next week, in Week 15, we're going to
look at some more applications of integration, really focusing on volume
calculations, which I think are a lot of fun because it will give us a chance to
think 3-dimensionally. And then, we've got the final exam and
that's it. So, hang in there, we've just got one
more week after this and then it's the end of the course.
We're going to make it.