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5.5 The Trapezoidal Rule Slide 2 I. Trapezoidal Rule A.) Area of a Trapezoid - Slide 3 B.) Approximate the area under the following curve from x = 1 to x = 4 using 6 subintervals of trapezoids. Slide 4 VISUALLY: Slide 5 TRAM: Slide 6 TRAM: Slide 7 C. Theorem: The Trapezoidal Rule To approximateusing trapezoids Where [a, b] is partitioned into n subintervals equal length Slide 8 D. Using the Calculator: Slide 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. Slide 10 Visually: Slide 11 Slide 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 Slide 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 Slide 14 Slide 15 II. Simpsons 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. Slide 16 II. Simpsons 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.