Day 11 in MAT227

Today:

• Announcements:
  • Just got back into town: how did it go?

• Today we're looking at section 6.2: Setting up integrals: Volume, Density, Average Value. What questions do you have about this topic, or any of our previous topics?
  • The difference in area between two curves
  • The last lab
  • Substitution
  • Net change as the integral of a rate
  • The Fundamental Theorem of Calculus, Part II
  • The Fundamental Theorem of Calculus, Part I (it's really that easy!)
  • anti-derivatives
  • Definition of the Riemann sum (a function of three variables! See p. 262).
  • Definition of the definite integral.
  • Properties of the definite integral.
  • Summation formulas
  • Limits of summations (power sums)
  • Putting these formulas into your calculator.
  • ???

• I'd like to take a little time to work a couple of examples: one standard, the other not so much.
  1. A standard volume problem
  2. An interesting traffic problem

• In both cases, the problem comes down to figuring what you want to "add up", in an integral of the form

• Next 25 minutes:

  You will undertake the following activity: Setting up integrals

• For the final 20 minutes, we'll switch to a class discussion of the proposed solution(s).