Unit route
Complete lessons in sequence, use diagnostic evidence to select a pathway, conduct the investigation, submit corrected work, and demonstrate mastery at 80% or above.
Weeks 15, 16, 17 · 7 college lessons
Advanced Applications of Integration
How do geometry, slicing, rotation, and metric formulas turn integral setup into defensible area, volume, length, and surface models?
Pathways
Lesson 01 · Week 15
Area Between Curves & Intersection Analysis
Finding intersections, ordering curves, and splitting intervals.
Lesson 02 · Week 15Volumes by General Slicing
Expressing volume as the integral of cross-sectional area.
Lesson 03 · Week 15Disks & Washers
Measuring radial cross-sections around an axis.
Lesson 04 · Week 16Cylindrical Shells
Using radius-times-height when shells simplify the setup.
Lesson 05 · Week 16Arc Length
Accumulating differential distance along a smooth curve.
Lesson 06 · Week 17Surface Area of Revolution
Accumulating circumference times differential arc length.
Lesson 07 · Week 17Method Selection, Units & Geometric Verification
Defending bounds, method, orientation, and reasonableness.