1. Chapter 6
Applications of Derivatives
Section 6.5
Trapezoidal Rule

2. Quick Review

3. Quick Review Solutions

4. What you’ll learn about
Trapezoidal approximations
Comparison to other numerical approximations
Bounding the error in the Trapezoidal Rule
… and why
Some definite integrals are best found by
numerical approximations, and rectangles are not
always the most efficient figures to use.

5. Trapezoidal Approximations

6. The Trapezoidal Rule

7. Simpson’s Rule

8. Error Bounds

9. Quick Quiz Sections 6.4 and 6.5x 1 4 6 7
f(x) 10 30 40 20

10. Quick Quiz Sections 6.4 and 6.5x 1 4 6 7
f(x) 10 30 40 20

11. Quick Quiz Sections 6.4 and 6.5

12. Quick Quiz Sections 6.4 and 6.5

13. Quick Quiz Sections 6.4 and 6.5

14. Quick Quiz Sections 6.4 and 6.5

15. Chapter Test

16. Chapter Test

17. Chapter Test
8. A diesel generator runs continuously, consuming oil at a gradually increasing rate until it must be temporarily shut down to have the filters replaced.
Give an upper estimate and a lower estimate for the amount of oil consumed by the generator during that week.
Use the Trapezoidal Rule to estimate the amount of oil consumed by the generator during that week.

18. Chapter Test

19. Chapter Test Solutions

20. Chapter Test Solutions

21. Chapter Test Solutions
8. A diesel generator runs continuously, consuming oil at a gradually increasing rate until it must be temporarily shut down to have the filters replaced.
Give an upper estimate and a lower estimate for the amount of oil consumed by the generator during that week. Upper = L; Lower = L
Use the Trapezoidal Rule to estimate the amount of oil consumed by the generator during that week. 4.2L

22. Chapter Test Solutions