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 18, 19, 20 · 7 college lessons
Physical, Engineering & Probability Applications
How does integration combine distributed force, mass, pressure, probability, and expectation into measurable system quantities?
Pathways
Lesson 01 · Week 18
Work by a Variable Force & Hooke’s Law
Integrating force over displacement.
Lesson 02 · Week 18Pumping Fluids & Distributed Lifting
Slicing fluid by depth and multiplying weight by lift distance.
Lesson 03 · Week 18Hydrostatic Force on Submerged Surfaces
Integrating pressure times width at depth.
Lesson 04 · Week 19Moments, Centroids & Centers of Mass
Using weighted averages of distributed mass.
Lesson 05 · Week 19Probability Density Functions
Using nonnegative integrals of total area one.
Lesson 06 · Week 20Expected Value, Variance & Risk Interpretation
Integrating outcomes weighted by probability density.
Lesson 07 · Week 20Engineering Model Assumptions, Sensitivity & Reporting
Documenting geometry, density, units, uncertainty, and limitations.