AP Calculus Trapezoidal Rule Name______
5 1. Use the trapezoidal rule to solve x 2 2 dx with n = 6. SHOW THE COMPLETE SETUP. 2
2. A vehicle’s aerodynamic drag is determined in part by its cross-sectional area, and all other things being equal, engineers try to make this area as small as possible. Estimate the cross-sectional area of James Worden’s solar- powered Solectria car at M.I.T. from the diagram below. Use only the middle region with left and right base = 0.
3. The table lists several physical measurements gathered in an experiment to approximate a continuous function 2 y = f(x). Approximate the integral f (x)dx . x 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0 y 4.32 4.36 4.58 5.79 6.14 7.25 7.64 8.08 8.14
4. A new park is being designed with a fishing lake included. The lake will be filled from a spill way branched off from the river that winds through the city. The city must keep the cost below $17,000 for building the lake. One company has made a bid to keep the cost below the $17,000. What is the maximum amount the company can charge per sq.ft.?
______5. A map of an ocean front property is drawn. What is its area? ______6. The data given are adapted from the August, 1991 issue of Road & Track magazine. They give the velocity v(t) of the $239,000 Lamborghini Diablo at time t seconds. Let x(t) denote the distance the car travels for time t, 0 ≤ t ≤ 10. Using the trapezoidal rule find x(10). Hint: Multiply your answer by 5280/3600 to change to feet.
t v(t)
0 0 mph 1 14 mph 2 27 mph 3 40 mph 4 53 mph 5 64 mph 6 70 mph 7 77 mph 8 84 mph 9 90 mph 10 96 mph t(hours) 0 1 3 4 7 8 9 L(t) (people) 120 156 176 126 150 80 0
______7. Concert tickets went on sale at noon (t = 0) and were sold out within 9 hours. The number of people waiting in line to purchase tickets at time t is modeled by a twice-differentiable function L for 0＃t 9 . Values of L(t) at various times t are shown in the table above.
Use a trapezoidal sum with three subintervals to estimate the average number of people waiting in line during the first 4 hours that tickets were on sale.
______8. The graph of a differentiable function f on the closed interval [-3, 15] is shown in the figure above. The graph of f has a horizontal tangent line at x = 6.
15 Find a trapezoidal approximation of f (t)dt using six subintervals of length t = 3. 3