Warmup was 2 indefinite integral problems revolving some reverse chain rule and the ln rule. Reviewed area/velocity/movement discussion from Friday before building up to the FTC part 2 conclusion involving evaluating a definite integral. In short, since the area under a velocity graph has units in meters, and the distance an object travels over time [a,b] can be found by subtracting the positions at these times, the area under a curve can be found by evaluating an antiderivative at the endpoints and finding the difference. Worked 2 examples, one showing the effectiveness of an earlier trapezoidal approximation and another using basic logarithm properties to produce a nice result.
Notes from board
Homework
p. 288 #5-20
check calcchat.com for help, also use MATH-9 on calculator to check numerical answer
can also use desmos function "INT" (no quotes) to call up a definite integral.
Resources
basis for second FTC if you're lost: link
basic definite integral evaluation; link
another definite integral example: link
Warm up was to evaluate a definite integral using the FTC part 2, resulting in a value of zero. This is because our bounds were symmetric about the origin and our function (sin(x)) was an 'odd' function. Went over definite integral homework, then worked on an AP free response problem relating to position-velocity-acceleration in the context of area under a given velocity graph. (The problem is worked out here if you were confused). Started a review activity we didn't have time for, so then we got the practice assessment and looked at it in broad conceptual terms.
Notes from board
Homework
do the practice assessment (blank copy) [SOLUTIONS]
Resources
write a definite integral from an infinite Riemann sum: link1 link2
write an infinite Riemann sum from a definite integral: link
rectangular approximation of definite integral: link
midpoint sum from a table: link
trapezoidal rule: link link2 (starts at 5:30)
finding exact value of definite integral using FTC2: link
evaluating a definite integral, simplifying with properties of logarithms: link
reverse chain rule examples link link 2, cool old australian guy