- Problem set 9 questions missing in 12th edition of Thomas
- Questions 1, 2, 5, maybe others
- Integral for question 2:
- Research weekend colloquium
- “Quantum Game Theory”
- Prof. Tom Cooney
- Today (November 13), 4:00 PM
- Newton 203
- Usual extra credit offer
- Problem set question 5 (washers)?
- Integrate in two pieces
- Integrate in two pieces
- Summary of section 15.5
- Partition of region into boxes?
- Triple integral includes z coordinate in integral
- e.g., … dz dy dx
- Finding x, y, z limits of integration
- Draw region
- Consider shadow in xy plane
- Lines from shadow through region suggest z limits
- Lines from x axis through shadow suggest y limits
- x ranges over all values that can cast lines into shadow
- Volume is triple integral over region of dV (see diagram above)
- Average value of f(x,y,z) over R is 1/V times integral of f over R
- Partition of region into boxes?
- Examples
- Volume between rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 1, and
z = x2 - y2 + 2
- Do it as a double integral rather than triple?
- What if (x,y) lies in triangle bounded by y = 0, x = 2-y, x = y?
- Integrate over y as outermost integral then x
- Integrate over y as outermost integral then x
- Do it as a double integral rather than triple?
- Volume between rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 1, and
z = x2 - y2 + 2
- Triple integration of non-trivial functions
- Line integrals
- Read section 16.1 up to but not including “Mass and Moment Calculations”
- (Page 938 through 1st half of 941 in 13th edition)