Took assessment on basic antiderivatives, reverse chain rule, and u-sub.
Homework
watch this video: link
Watch the video below and do #53-58 on p 252 (digital copy)
Passed back tests from Monday and learned about finding the value of C using given information after integrating, in the context of motion.
Notes from board
Homework
be sure to watch the video above for more info and do #53-58 on p 252 (digital copy)
Warm up was two more indefinite integrals that required some creativity to solve. Went over homework briefly (don't worry if you found it too hard, as long as you can do what was in the snow day video and DS Weds you'll be okay for now) we then moved onto the major topic of integral calculus, the question of finding areas of weird spaces under curves. Reviewed how limits allow us to make mathematical concepts dynamic instead of static and how they are central to both derivatives and the concept of using rectangles to move from approximating area to getting the exact area. Also reviewed sigma notation and how it functions, leading up to the idea of the infinite sum.
Came up with a systematized way of setting up and finding areas of rectangles under curves using sigma notation. This is called a Riemann sum and is an estimate of the area under a curve when using a finite number of rectangles. With a limit, the number of rectangles can approach infinity which leads to the exact area through something called the "definite integral" which is defined as the limit of a Riemann sum. Since definite integrals require some additional calculus, we can presently only approximate them using finite sums with finite subintervals, which raises of the question of how to determine the height of the rectangle. Two common ways are to use either the left or right endpoint of each subinterval and systematically find their height that way. This is called an LRAM or RRAM estimate. Worked out LRAM together for a curve, and started RRAM before the bell rang.
Notes from board
Homework
p. 263 #25-30, 33, 34 (due Tuesday)
Resources
see the video under "Monday" to explain the whole concept from today better
LRAM and RRAM example by me :) link
another RRAM example by me :) link
more good examples, by another person: link