Monday
Today was a full B-day meeting. Warm up on properties of definite integrals. Went over hw, then passed out 3 AP free-response questions dealing with integration and area. Everyone did 1 problem in small groups, then returned to their table and explained their problem to their tablemates. The blank and worked out versions of these problems are linked below. Started to talk about area between curves but didn't get very far -_-
Blank AP Problems
Worked out AP Problems
Homework
none
Did several review problems starting from a given f-prime function related to quotient rule, tangent lines, relative extrema, finding c and definite integration. Also did a warm up related to using the trapezoid approximation method with a table. Looked at finding area under the curve using a definite integral, albeit with an integrand that required some simplification. Then looked at how to find areas that are adjacent not to the x-axis but to the y-axis. Finally looked at how to find area between two curves which boils down to the integral of the top function minus the bottom function over the intervals indicated by their intersection (or other given boundaries). Sometimes you have to use multiple integrals to find the total area if the functions intersect and "switch places" and sometimes you can use symmetry to simplify calculations.
Notes from board
Homework
This handout [blank] [numerical answers]
confused?? check out this video!!!
Resources
quotient rule: link
write equation of tangent line: link
finding relative extrema: link
finding C: link
trapezoid rule from a table: link
simple area under a curve: link
area between two curves, unified region: link link 2
area between two curves: split region, trig: link
Warm up was two non-calculator multiple choice AP problems, one dealing with area under the velocity graph as distance traveled (so long as velocity remains positive) and finding the area under the curve. Worked in pairs on AP FRQ problems related to area between curves on chart paper. Then introduced the idea of the net change theorem, a re-arrangement of the FTC2 which says that the future value of a changing quantity is equal to the starting value plus the accumulation of all the changes in between the starting and the future value. We will see much more of this in the future.
Notes from board
problems worked on by pairs
Homework
p 313: #41-55, 63-70 [Due Wednesday]
Resources
properties of definite integrals: link 1 link 2
area under the curve: link
evaluating a definite integral: link
Reverse chain rule example link