Integrals over General Regions

Return to List of Lectures

Previous Lecture

• Misc
  • Actuary Club
    • Meeting Wednesday 4/6, 2:30 - 3:30
    • South 338
    • Questions to bjv2
  • REU Talk
    • Stephanie Allen re identifying social groups in economic need
    • Wednesday April 6th, 3:30 pm
    • South 328
    • Snacks
    • Usual extra credit for write-ups
• Questions?
• Integration
  • General regions: section 15.2
    • Definition of integral over an arbitrary region
      
    • Finding bounds aka limits of integration
      • Use either vertical cross sections or horizontal
      • Sketch, find x- and y limits
    • Properties of double integrals
      • Domination?
        
  • Area and average: section 15.3
    • Area formula
      
    • Average formula
      
  • Examples
    • Integrate x+y over 0 ≤ x ≤ 1 and 0 ≤ y ≤ x²
      • What is the region?
      • What would this look like if order of integration was reversed?
        
      • Check both orders of integration in muPad to see that they are the same, and that muPad can do general multiple integrals in the first place
        
    • What is area between y = 3x² and y = -3x?
      
  • Problem set
• Next
  • Practice finding bounds
  • And extending ideas so far to triple integrals
  • Read section 15.5

Next Lecture