Section 7.3, 7.4

1) How does integration figure into calculating physical work? What is it that makes the use of integration necessary in computing work?

2) What is Hooke's law?

3)What is Newton's law of gravity?

4) Give an example of a separable differential equation and an example of a non-separable differential equation. Briefly what does the book suggest as a general approach for solving the separable DE?

5) Was there anything specific in this section that was confusing to you? Is there any specific (or general) question you would like to have answered?

Section 7.1, 7.2

1.True or false: When you are using integration to measure the area between two curves and one or both of these curves falls below the x-axis, the integral counts this as "negative" area.

2. In finding volumes by cross sectioning, what do we assume about cross sectional area when Delta x (thickness) is small? What is the volume of such a section, approximately?

3.What are the cross sections of solids of revolutions like?

4. What is the area of the washer? (Your answer should include the terms "inner radius" and "outer radius")

5. Was there anything specific in this section that was confusing to you? Is there any specific (or general) question you would like to have answered?

Section 6.1, 6,2

1. What does the word "error" mean in connection with approximating sums for integrals?

2. If a function f is decreasing over an interval, what can you say about the relationship between Rn and Ln on that interval? Why does this relationship hold?

3. If a function f is concave up over an interval, what can you say about the relationship between Tn and Mn on that interval? Why does this relationship hold?

4. The Simpson's rule can be thought of as a "weighted average" of two other sums. What are they? Which one gets more weight and why?

5. Do the error bounds for Rn and Ln depend on the first or the second derivative of the function?

6. Do the error bounds for Mn and Tn depend on the first or the second derivative of the function?

7. Was there anything specific that was confusing to you?

Section 5.6, 5.7

1. Which do you think is the most accurate way to approximate an integral: Left Sums, Right Sums, or Trapezoid Sums? Why?

2.Which of the following is not a Riemann sum? Left Sum, Right Sum, Midpoint Sum, Trapezoid Sum.

3. What is a regular partition? Can a Riemann sum use a partition that is not regular?

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

Section 5.1,5.2,5.3 from OZ (Our Calculus texbook by Ostobee & Zorn)

If you are comfortable with the above sections, go ahead and read Section 5.6.