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Determining the volume and surface area of solids of revolution. 3. Advanced Engineering Topics Centroids and centers of gravity. Calculating Moments of Inertia and the radius of gyration. Basic Integration: Standard results

Module 1: Indefinite Integrals

• Basic Integration: Standard results, integration of algebraic functions.
• Transcendental Functions: Integration of exponential, logarithmic, hyperbolic, and inverse trigonometric functions.
• Advanced Techniques:

  7. Typical pitfalls and how to avoid them

  • Not simplifying integrand first — always simplify/algebraically reduce.
  • Choosing poor u/dv in parts — use LIATE/ILATE heuristics.
  • Forgetting +C for indefinite integrals.
  • Mishandling limits in improper integrals — convert to limits before evaluating.
  • Incorrect region bounds for multiple integrals — sketch region carefully.