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 6, 7, 8 · 7 college lessons
Trigonometric Integrals & Trigonometric Substitution
How do identities and right-triangle substitutions convert trigonometric powers and radical forms into integrable structure?
Pathways
Lesson 01 · Week 6
Powers of Sine and Cosine
Using odd-power separation or even-power reduction.
Lesson 02 · Week 6Powers of Tangent and Secant
Using sec²x or sec x tan x factors and identity conversion.
Lesson 03 · Week 6Products, Multiple Angles & Identity Selection
Rewriting products before integration.
Lesson 04 · Week 7Substitution for √(a²−x²)
Using x=a sin θ and a reference triangle.
Lesson 05 · Week 7Substitution for √(a²+x²)
Using x=a tan θ and secant structure.
Lesson 06 · Week 8Substitution for √(x²−a²)
Using x=a sec θ and careful domains.
Lesson 07 · Week 8Back-Substitution, Domain Analysis & Verification
Reconstructing x-forms and checking interval conditions.