Unit 03 Honors / Extended Practice

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Honors / Extended pathway

Trigonometric Integrals & Trigonometric Substitution

Deeper proof, synthesis, parameter analysis, and unfamiliar applications.

1. Evaluate ∫sin³x cos²x dx.

2. Which statement best describes the central reasoning in Powers of Sine and Cosine?

3. Evaluate ∫tan³x sec²x dx.

4. Which statement best describes the central reasoning in Powers of Tangent and Secant?

5. Evaluate ∫sin(3x)cos(2x)dx.

6. Which statement best describes the central reasoning in Products, Multiple Angles & Identity Selection?

7. Evaluate ∫dx/√(9−x²).

8. Which statement best describes the central reasoning in Substitution for √(a²−x²)?

9. Evaluate ∫dx/(x²+4)^{3/2}.

10. Which statement best describes the central reasoning in Substitution for √(a²+x²)?

11. Evaluate ∫dx/√(x²−25).

12. Which statement best describes the central reasoning in Substitution for √(x²−a²)?

13. For x=3tanθ, express secθ in x.

14. Which statement best describes the central reasoning in Back-Substitution, Domain Analysis & Verification?

β Beta Program