Went over reverse chain rule hw solutions. Answer questions on linearization. Took assessment on basic antiderivatives, related rates, and linearization. Learned some new integrals, including these (added to formula booklet). Looked at integral of 1/x in some detail--will do in more depth on Weds.
Homework
Short assessment on reverse chain rule integrals on Wednesday
Due Friday:
p. 302 #47-50 (I-A2b)
p. 251 #35-42 (I-A3)
Worksheet #1-10 (worksheet linked here)
Resources
see previous post, duh
finding C: starts at 19:20 link
challenging but great pos/vel/accel problem: link
U-sub example and reverse chain rule example in DS. Reverse chain rule assessment to start class, looked at advanced anti derivative rules examples like those involving the natural log, some trig examples, and inverse trig examples. Notes here.
Homework;
p. 302 #47-50 (I-A2b)
p. 251 #35-42 (I-A3)
Worksheet #1-10 (worksheet linked here) [solutions here]
Assessment on Monday covers: u-substitution, finding C, and advanced antiderivatives.
Resources:
inverse trig integrals: link
more inverse trig: link
Advanced antiderivatives video made my me just for youuu!! link
Dove right into definite integration, Looked at the difference between it and indefinite integration (antidifferentiation). The latter which we have done a lot of work with results in an answer that is a family of functions. This new kind results in a single numerical answer. How do you get that numerical answer? See here for a quick demo: link
A quick review of sigma notation followed. see this video here for a summary: link
Then transitioned to finding areas under curves and how to approximate this best. This basically involves geometric shapes like trapezoids or rectangles and using them to cover up most of the space. How do you improve the approximation? Use more rectangles. We did the simple case illustrated here for those who were confused: link
We then looked at how you would set up the process not for 4 rectangles but for n rectangles. If n was big, that would be a really good approximation. We did what is illustrated here: link
That brought us to the realization that the sigma-sum of f(x)delta_x is essentially the same notation as integral of f(x) dx. For those who did not understand this "discovery" see here: link
And then right as class ended, we looked at the connection between area and antiderivatives. That is covered here: link
Here are the notes from the board
Here is a clean copy of the worksheet/outline
Here is a worked-out copy of the outline
Homework:
- finish the stuff assigned last Monday if you haven't yet
- FYI: assessment Monday on u-substitution, finding C, and advanced antiderivatives
New hw : Watch and take notes on this single video: