1. 5.5
Trapezoidal Rule

2. Quick Review

3. Quick Review Solutions

4. What you’ll learn about
Trapezoidal Approximations
Other Algorithms
Error Analysis
Essential Question
How do we find definite integrals that are not
best found by numerical approximations,
and rectangles are not always the most
efficient figures to use?

5. Trapezoidal Approximations

6. The Trapezoidal Rule

7. Example Using Trapezoidal Rule
Use the Trapezoidal Rule with n = 4 to approximate the value of the integral. Use the concavity of the function to predict whether the approximation is an overestimate or an underestimate.
Concave Down
underestimate

8. Simpson’s Rule

9. Example Using Simpson’s Rule
Use Simpson’s Rule with n = 4 to approximate the value of the integral. Find the integral’s exact answer to check your answer.

10. Error Bounds
and

11. Pg. 312, 5.5 #1-19 odd