Triple integral and polar/cylindrical coordinates

  1. Introduction
    • Explanation of type 2 region in triple integral
    • Ordering of variables in triple integral for type 2 region
  2. Scenario of Polar Region
    • Explanation of domain of integration in polar region
    • Conversion of variables in polar coordinates
  3. Example: Triple Integral Over a Tetrahedron
    • Explanation of the problem
    • Drawing and explanation of the tetrahedron
    • Setting up the triple integral for the tetrahedron
    • Explanation of the bounds of integration
  4. Example: Volume of a Right Pyramid
    • Explanation of the problem
    • Drawing and explanation of the pyramid
    • Setting up the triple integral for the pyramid
    • Calculation of the volume of the pyramid
  5. Example: Triple Integral Over a Solid
    • Explanation of the problem
    • Discussion of the difficulties in setting up the integral
    • Suggestion of a different approach using polar coordinates
    • Setting up the triple integral in polar coordinates
    • Calculation of the triple integral
  6. Conclusion
    • Recap of the lecture
    • Encouragement for questions and participation
    • Acknowledgement of student participation