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Strategy Visualization Step-by-Step Layout Single Step Zoom
Ring-by-ring
Slice-by-slice
Board-by-board
r
p
x
dp
dx
dr
Strategy Visualization Step-by-Step Layout Calculus Lingo
Ring-by-ring
Slice-by-slice
Board-by-board
Ring-by-ringTimelapse
Shell-by-ShellX-Ray
Plate-by-plateTimelapse
Circumference Area Volume Surface area
Derivative Symbol Mindset
Think about the resulting step-by-step pattern
Think about the actual ratio of changes
Infinity
…
Image source: wikipedia
The Derivative
1. Choose an interval 2. Find the raw change
3. Find the rate of change4. Make your model perfect
F’s changes
G’s changes+Simplifies to
Scenario With 2 Parts
F G+
F G*
F G^
F G/
…
Two Perspectives To Consider
Strategy Visualization Step-by-Step Layout Single Step Zoom
Ring-by-ringTimelapse
r dr
2πr
Symbolic Description Solution Notes
Work backwards to the integral.
that meansIf
Symbolic Solution Notes
Write height in terms of x
Work backwards to find integrals
Find volume at full radius (x=r)