1. Homework Homework Assignment #1 Read Section 5.2 Page 308, Exercises: 1 – 25(EOO) Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

2. Homework, Page 308 1. An athlete runs with a velocity of 4 mph for a half-hour, 6 mph for the next hour, and 5 mph for another half-hour. Compute the total distance traveled and indicate on a graph how this quantity can be interpreted as an area. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

3. Homework, Page 308 5. Compute R 6, L 6, and M 3 to estimate the distance traveled over [0, 3] if the velocity at half-second intervals is as follows: Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

4. Homework, Page 308 9. Estimate R 6, L 6, and M 6 for the function in Figure 15. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

5. Homework, Page 308 Calculate the approximation for the given function and interval. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

6. Homework, Page 308 Calculate the approximation for the given function and interval. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

7. Homework, Page 308 Calculate the approximation for the given function and interval. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

8. Homework, Page 308 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

9. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Jon Rogawski Calculus, ET First Edition Chapter 5: The Integral Section 5.2: The Definite Integral

10. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Georg Riemann was 19 th century German mathematician whose memory is honored by the naming of Riemann Sums. Riemann Sums are a generalization for the RAM methods discussed in the previous section. The widths may vary and the value of x for which f (x) is found need not be consistent rectangle to rectangle.

11. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company The largest subinterval in a Riemann sum is known as the norm of the partition.

12. Example, Page 321 16.Describe the partition P and the set of intermediate points C for the Riemann sum shown in Figure 16. Compute the value of the Riemann sum. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

13. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company If a rectangle falls below the x-axis the sign of its area is negative.