Unit 05 Honors / Extended Practice

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Honors / Extended pathway

Improper Integrals & Numerical Integration

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

1. Evaluate ∫₁^∞1/x² dx.

2. Which statement best describes the central reasoning in Infinite-Interval Improper Integrals?

3. Evaluate ∫₀¹x^{-1/2}dx.

4. Which statement best describes the central reasoning in Unbounded Integrands on Finite Intervals?

5. Does ∫₁^∞1/(x²+1)dx converge?

6. Which statement best describes the central reasoning in Comparison for Improper Integrals?

7. Determine ∫₁^∞x^{-3/2}dx.

8. Which statement best describes the central reasoning in p-Integrals & Threshold Reasoning?

9. Use T₂ for ∫₀²x²dx.

10. Which statement best describes the central reasoning in Midpoint & Trapezoidal Rules?

11. Use S₂ for ∫₀²x²dx.

12. Which statement best describes the central reasoning in Simpson’s Rule & Error Structure?

13. Why is ∫₀¹e^{-x²}dx usually evaluated numerically?

14. Which statement best describes the central reasoning in Adaptive Strategy, Nonelementary Integrals & Validation?

β Beta Program