1. 5.5 The Trapezoidal Rule

2. I. Trapezoidal Rule A.) Area of a Trapezoid -

3. B.) Approximate the area under the following curve from x = 1 to x = 4 using 6 subintervals of trapezoids.

4. VISUALLY:

5. TRAM:

6. TRAM:

7. C. Theorem: The Trapezoidal Rule To approximateusing trapezoids Where [a, b] is partitioned into n subintervals equal length

8. D. Using the Calculator:

9. II. Examples 1. Use 5 trapezoids to approximate the area bounded by the curve of, the x- axis, and the vertical lines x = 0 and x = 5. Write out each term of the summation and confirm on your calculator.

10. Visually:

12. 2. The table shows the velocity of a car traveling on a highway at different times. Use TRAM to estimate the total distance traveled over the time interval. t(sec)01020304050607080 v(t) (ft/sec)02545607565606550

13. 3. The table shows the reading of outdoor temperatures from noon to midnight for a certain day. Estimate the average temperature for the 12 hour interval using the trapezoidal rule. Time12 PM 123456789101112 AM Temp63656668706968 6564625855

15. II. Simpson’s Rule Given a nonnegative function f (x), i.e., f (x) > 0, on [a, b]. Find the area bounded by the curve, the x- axis, and the vertical lines x = a and x = b.

16. II. Simpson’s Rule Given a nonnegative function f (x), i.e., f (x) > 0, on [a, b]. Find the area bounded by the curve, the x- axis, and the vertical lines x = a and x = b.