[MUSIC]. Welcome back to Calculus One.
And welcome to Week 15 of our time together.
We've been at this since January, and this is it, this is the last week of the
course. Where are we?
Last week in Week 14, we were working at techniques of integration and the
technique that we focused on was integration by parts.
This week in Week 15 we're looking at an application of integration, but which
application? There's so many applications of
integration that we could be looking at. We could fill up a whole Calculus Two
course with various applications of the integral.
The application that we've picked is volume.
I think it's a ton of fun, to use integrals to calculate the volumes of
solid three dimensional objects. It's fun because it gives us a chance to
think geometrically, to think three-dimensionally, but I also think
it's important historically. You know, thousands of years ago, the
first inklings of a definite integral appeared, you know?
People were thinking about taking objects and slicing them into really thin pieces,
say infinitesimal pieces, and adding up all of those infinitesimal pieces.
And the idea is really, really old. So, I think it's appropriate that we end
this course with something at the very beginning of humankind's grasping towards
the definite integral. We're going to end this course with some
volume calculations. It's also appropriate that we end this
course for the final exam. The final exam is available right now,
and you got until the beginning of May to finish it.
Good luck.