5 5 The Trapezoidal Rule I Trapezoidal Rule

5. 5 The Trapezoidal Rule

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

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

VISUALLY:

TRAM:

TRAM:

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

D. Using the Calculator:

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.

Visually:

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) 0 10 20 30 40 50 60 70 80 v(t) (ft/sec) 0 25 45 60 75 65 60 65 50

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. Time 12 PM 1 2 3 4 5 6 7 8 9 10 11 12 AM Temp 65 66 68 70 69 68 68 65 64 62 58 55 63

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 xaxis, and the vertical lines x = a and x = b.

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 xaxis, and the vertical lines x = a and x = b.