No warm up. Took assessment on basic antiderivatives and u-substitution. Passed out worksheet for practicing MRAM and TRAP (midpoint rectangles and trapezoid approximation methods).
Today's assessment solutions
Homework
finish #1-8 on this worksheet
Resources
Example of how to find a midpoint approximation and trapezoid approx. [Made by me :)] LINK
Warm up on 3 indefinite integral problems. Passed back assessments, worked through finding C example dealing with position function given velocity and initial position. Went over worksheet answers on MRAM and TRAP approximations for definite integrals, then looked at how to find an integral approximation when given a table of values.
Introduced idea of area under a rate function as an accumulation of a quantity. Worked through accumulation functions using geometry to develop A(x) area functions under f(x) and then took derivative A'(x) and returned back to f(x). So if an area function becomes the boundary curve by derivative, then it stands to reason that an antiderivative of a boundary curve gives the area. This is the Fundamental Theorem of Calculus pt 2. Worked through an example of finding a definite integral.
Notes from board
Homework
p288 #6-27 [multiples of 3]
Resources
simple finding C: link
more finding C: link
LRAM and RRAM with a table: link
basis for FTC2: link
basic definite integral evaluation; link
another definite integral example: link
Warm up reviewed writing the equation of a tangent line (product rule involved) and then finding the position of an object given the acceleration function and initial velocity and position. Spent most of class in pairs/groups working on taking definite integrals and making left rectangle approximations, trapezoid approximations, and using the FTC 2 to find the exact values of the integrals.
Homework
Finish this worksheet for Wednesday [Answers]
Do it by hand please! Using the FTC 2, not just typing in the calculator :)
Assessment will be in class Weds, will get practice on Monday
Resources
writing the equation of a tangent line: link
find position given acceleration: link
finding rectangular approximation: link
finding trapezoid approximation: link
finding exact value of definite integral using FTC2: link