2. A Quick Review of Math 200  Calculus rests on 3 critical ideas/concepts: Total accumulated change Instantaneous rates of change Limit

3. Rate of Change…  Relates to slope in the real world  By using limit the “Rise/Run” becomes the Newton Quotient  And the rest… Max/Min Max/Min Related rates Related rates Differential Equations Differential Equations

4. Perhaps one of the most important graphs in history! Slope is about 1.4 ppm/year (1958,315)

5. Snapshot of Earth Breathing!

6. Example: a drug is released into a patients blood stream at a rate given by  g/minute. How much drug does the patient receive in 4 minutes? Total Accumulated Change…  Relates to the idea of area in the real world Units are  g/min

7. Working with Integrals…  Pay attention to 5.2 and 5.4 in text Substitution: simplest of the methods (Chp 7.1) Substitution: simplest of the methods (Chp 7.1) Integration by parts (coming in Chp 7) Integration by parts (coming in Chp 7) etc etc

8. Which of the following are good candidates for substitution?

9. Areas Between Curves Section 6.1

10. Some warm ups…  What is the area between the x-axis and the graph of  When is an area “equal to” an integral?

11.  What’s the area between the x-axis, the lines x = 0 and x = 2 and the graph of the function  What’s the area between the y-axis and the above function (x = 0 and x = 2)?  What’s the area between the curves y = x 3 and y = x?

12.  Checklist of things to watch for when finding areas between curves… Can we develop a strategy?

13. Some examples…  Pg 331: 68,71,72