Continued with the idea of area as the sum of rectangles, but this time horizontally oriented. Looked at area between curves from a "dy" perspective with the paradigm being "right minus left" to find the horizontal width of the rectangles with thin 'dy' height. Then submitted AP mult choice answers via this link. BTW here are the solutions: link
Notes from board
Homework
backside of area handout #7-12 (blank copy here)
Resources
DY area between curves: link
DX area between curves power rule and trig functions
Warm up was to find the second derivative of accumulation functions. Worked through a net change/accumulation problem from an AP test dealing with water volume in a tank both being added and pumped out. Reviewed the MVT briefly and saw how it leads to the MVT for Integrals which calculates the average output value a function has over an interval. Did an example, then got practice test.
Notes from board
Homework
start the new practice assessment (blank copy) (SOLUTIONS)
real assessment is on Monday
Resources
connection between MVT and the average value: link
concept + procedure of average value (and MVTi) link
No warm up but did a few AP-test style example problems dealing with various topics on the Q3 last assessment including area between curves (including using the calculator to find intersection points), net change, trapezoid sum from a table, and interpreting average value.
Notes from board
Homework
start the new practice assessment (blank copy) (SOLUTIONS)
real assessment is on Monday
Additional Problems in book for help/practice
I-A4b area between curves: p. 442: much of the page is good
I-U7 prop of definite integrals: p. 274 #41-44
I-U4: FTC algebra: p. 290 81-92
I-U9: FTC graphically: p.290 73-74; p. 274 #47-48
I-A7b: Net Change: p. 291 #103-104
I-A7a: Average Value:p. 288: #51-55
I-U3a: LRAM/RRAM: p. 263 #33-36
I-U3c: Riemann Sum from Table: p. 274 #45-46
I-A1a: Basic Antiderivatives: p.312 #1-8
Review Resources:
area between curves: link1 link2 how to find intersections
properties of def integrals: link (starts at 4:04) link2 (lots of ex)
FTC Algebraically: taking derivatives analysis using derivative
FTC Graphically: link1 link2
Net change: link (part a only)
Average Value: link
Average Value, interpretation: link (starts at 2:16)
Rectangular Approximation Method: link under vs over
Trapezoid rule from table: constant intervals changing intervals
Basic Antiderivatives: link1 link2 link3 link4