2. Multiple- Choice, Section I Part A Multiple- Choice, Section I Part B Free- Response, Section II Part A Free- Response, Section II Part B # of Questions 281724 Time Allowed 55 minutes50 minutes30 minutes60 minutes Calculator Use NoYes No Format of AP Exam (As of 2011)

3. 6.1 Area Formula The area between 2 continuous curves f(x) and g(x), where f(x)  g(x) for all x is:

4. Steps to follow: How to find the area: 1. Graph the region 2. Draw a generic rectangle. 3. Set up the integral. (Think high minus low) 4. Integrate!

5. 6.2 Volume Volume by disk dx Volume by disk dy Volume by Washers dx Volume by Washers dy Volume by different axes. Volume by cross section

6. 6.2 Volume by Rotation Let’s look at one cross section. A= A Big Circle – A Little Circle or A= R 2 -r 2 So, the formula for volume is: R r

7. 6.2 Volume by cross section A(x) is the area of the cross section in terms of x

8. 6.4 Average Value Theorem: If f is continuous on [a,b], then there exists a number c in [a,b] such that:

9. Review of Ch. 7 topics Slope fields Differential Equations Differential Equations with initial values

10. 7.2 Slope Fields Slope Field: A graphical representation of tangent lines to the family of solutions to a differential equation.

11. 7.3 Diffy Q’s Solve the differential equation Steps to an initial Value Problem: 1. Separate 2. Integrate 3. Plus C 4. Solve, plug in initial value before solving for y.

12. Get out any ASGN not stamped

13. ASGN Chapter 6,7 at a glance

14. Calculator Skills Graph a function Find a zero Graph a derivative Find an intersection Store a value Evaluate a function  g(5) Evaluate a derivative  g‘(6) Evaluate an integral  Calculate the area between curves.

15. 6.1 Area Graph the following function: 1. Set up the integral for the area of region bounded by the above functions.

16. An example you say?

17. 2. Set up the integral for the volume when rotated about the x-axis 4. Set up the integral for the volume when rotated about the line y=8

18. 5. Set up the integral for the volume generated by cross sections in the shape of squares. 6. Set up the integral for the volume generated by cross sections in the shape of semicircles. Volume by Cross sections

19. Now, we can solve for the value c, on the interval [a,b] 1. Calculate the average value over the given interval: 2. Set the ORIGINAL function equal to the average.

20. Solution (cont’d) y x y x-2012 2 1 0 -2 y = 3x

21. 7.2 Slope fields Using the provided grid, Sketch the slope field for the differential equation y = 3x.

22. Solution (cont’d) y x y x-2012 2-6-3036 1-6-3036 0-6-3036-6-3036 -2-6-3036 y = 3x

24. An example you say? Solve the differential equation

25. Solution (cont’d) Separate Integrate Plus C Solve

26. 7.3 Differential Equations Steps to an initial Value Problem: 1. Separate 2. Integrate 3. Plus C 4. Solve