Please enable JavaScript.
Coggle requires JavaScript to display documents.
Integrals - Coggle Diagram
Integrals
Anti-differentiation
reverse/opposite of differentiation
low level thinking
correct notations used
careful when using externally sourced practice material!
use correct formulae
what can students have on their notes page (cheat sheet)
integrate with natural logs
need to have already covered log laws
Prerequisite knowledge
integrate trig functions
means you have to have already covered all trig functions and their graphs
use linearity
"glue two integrals together"
order of operations
determine indefinite integrals
analogous to "subbing something in" in algebra
identify families of curves
thinking graphically
Just because the graph looks the same, does the equation look the same? and vice versa?
See lesson #2 flashcard activity
find f(x) given f'(x) and initial condition
need a good grasp of algebra and thinking flexibly
Applications
calculate total change by integrating rate of change
introduces new notation
calculate area under a curve
See lesson plan #1
calculate areas between curves
what area is between the road and the curve?
find displacement for given velocity
determine location given linear acceleration
projectile motion questions
Definite integrals
estimating area under a curve
definite integral as a sum of integrals
applying additivity and linearity of definite integrals
Fundamental theorem
Geometric proof
use to calculate definite integrals
