Day 14 in MAT229

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Announcements:
- Your Lab 3 grading is in process.
- Week 4. Remember we didn't have a weekly assignment week 3, because of the exam; Hence, this week we encounter weekly Assignment #3: due Monday, 2/8
  (here it is as a .nb)
Today we begin a section on Integration by parts.
- First of all, the big picture: integration by parts is just the product rule backwards. This integration technique, like all integration techniques, is really just a differentiation technique in reverse.
  Consider the method of u-substitution, for example. That's just the chain rule in reverse.
- We've already seen how important "thinking backwards" (or by reflection) is:
  - Inverse functions are reflections of one-to-one functions over the line $y=x$;
  - Properties of logs are really reflections of properties of exponentials;
  - Every time you learn a new derivative, you can solve a new integral;
  Have you ever watched "Dancing with the Stars"? You ever watch ballroom dancing?
  Here's a video clip of Fred Astaire and Ginger Rogers. They say Fred Astaire was pretty good (well, "the best dancer ever"); but Ginger Rogers did everything Fred did, only backwards (and in heels...).
- One new anti-derivative we can get using this technique is the anti-derivative of arctan.
- Here are our materials for today:
Links:
- Wolfram's Alpha is sometimes pretty helpful.

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