Calculus 2 :

Section 6.5: Problem 1 [1 point) Given the following integral and value of n, approximate the following integral using the methods indicated (round your answers to six decimal places): 1 f e'dz,n = 4 i] (a) Trapezoidal Rule Cl (n) Midpoint Rule C] (c) Simpson's Rule Cl Section 6.5: Problem 11 (1 point) Estimate ( cos(r?) da using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4. Give each answer correct to five decimal places. (a) T4 = (b) MASection 6.5: Problem 2 (1 point) A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see table). Use Simpson's rule to estimate the distance the runner covered during those 5 seconds. t (s 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 v (ft/s) 0 2.15 3.4 5.2 6.95 7.75 8.5 10.1 10.85 10.95 10.95 Estimated distance:Section 6.5: Problem 3 (1 point) Consider the integral approximation To of Jose i dx. Does 720 overestimate or underestimate the exact value? O A. underestimates O B. overestimates Find the error bound for 720 without calculating I7 using the result that M(b - a)3 Error (TN) 12N2 where M is the least upper bound for all absolute values of the second derivatives of the function 3e 7 on the interval [a, b]. Error(T20)Section 6.5: Problem 4 (1 point) ATTEMPT NOT ACCEPTED -- Please submit answers again (or request new version if necessary). Use six rectangles to find an estimate of each type for the area under the given graph of f from = = 0 to x = 12. 1. Take the sample points from the left-endpoints. Answer: Ls = 2. Is your estimate Is an underestimate or overestimate of the true area?|Overestimate 3. Take the sample points from the right-endpoints. Answer: R6 = 4. Is your estimate /46 an underestimate or overestimate of the true area?|Underestimate v 5. Take the sample points from the midpoints. Answer: Mo =Section 6.5: Problem 5 (1 point) ATTEMPT NOT ACCEPTED -- Please submit answers again (or request new version if necessary). Use four rectangles to find an estimate of each type for the area under the given graph of f from = = 1 to r = 9. 1. Take the sample points from the left-endpoints. Answer: LA = 2. Is your estimate 4 an underestimate or overestimate of the true area? Underestimate v 3. Take the sample points from the right-endpoints. Answer: R4 = 4. Is your estimate Is an underestimate or overestimate of the true area? |Overestimate 5. Use the Trapezoid Rule with n = 4. Answer: Ti = 6. Is your estimate 74 an underestimate or overestimate of the true area? |OverestimateSection 6.5: Problem 6 (1 point) The graph of a function f is given below. Estimate Sof(x) da using four subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints. (a) fo f(x) di = (b) So f(x) dx ~ (c) So f(x) dr ~ 0 1 XSection 6.5: Problem 7 (1 point) Given the following graph of the function y = f(I) and n = 6, answer the following questions about the area under the curve from = = 0 to = = 6. - 110 -1 1. Use the Trapezoidal Rule to estimate the area. Answer: To = 2. Use Simpson's Rule to estimate the area. Answer: 56 =Section 6.5: Problem 8 (1 point) Estimate the area under the graph in the figure by using (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule, each with n = 4. 801 2 3 4 x