11. [40.16 Points] DETAILS SCALCETQ 7.7.020. OHOO Submissions Used MY NOTES ASK YOUR TEACHER 2 (a) Find the approximations T10 and \"10 for] 17 EU" dx. [Round your answers to six decimal places.) 1 T10 \"10 = |:| (b) Estimate the errors in the approximations of part [a] using the smallest possible value for Kaccording to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) new : E w s E (c) Using the values ofK from part (b), how large do we have to choose :1 so that the approximations Tn and Mn to the integral in part (a) are accurate to within 0.0001? Need Help? _ This module allows you to estimate the value of a denite integral for a variety of different functions. You can interpret a denite integral graphically as the net area under the graph of a function. In other words, you look at the area enclosed by the graph of the tundion and the xaxis, and any area below the xaxis is subtracted from the area above the .xaxis. You can use Riemann sums to estimate the net area, where you approximate the enclosed region with redangles using left or right endpoints or midpoirs to determine the height, or you than select Simpson's Rule or the Trapezoidal Rule. In each case, the module will compute the estimated value and display a graph of the area computed. You can improve the approximation by increasing the number of subintervais, and you can see the error in the estimated value both graphically and numerically. Slmulaon BExertise Use Simpson's Rule with 10 subintervals to estimate the area under the graph ofy= U.2X2 for 2 s XS 4. E Explain why the error is exactly [1, I This answer has not been graded yet. 10. [40.16 Points] DETAILS SCALCETB 7.7.019.MI. Oil 00 Submissions Used MY N DTES ASK YOUR TEACHER | Do the following with the given information. 1 f 13 cosxz) dx l] (a) Find the approximations T3 and M3 for the given integral. (Round your answer to six decimal places.) (b) Estimate the errors in the approximations Ta and M3 in part (a). (Use the fact that the range ofthe sine and cosine functions is bounded by :1 to estimate the maximum error. Round your answer to seven decimal places.) IETI |:| IEMI e |:| IA (c) How large do we have to choose n so that the approximations Tn and Mn to the integral are accurate to within 0.0001? [Use the Fact that the range of the sine and cosine functions is bounded by :1. to estimate the maximum error.) Neee Help? 14. [10.19 Points] DETAILS SCALCETQ 7.7.030. 01100 Submissions Used I MY NOTES I ASK YOUR TEACHER I The widths (in meters) of a kidneyshaped swimming pool were measured at 2meter intervals as indicated in the gure below. Use Simpson's rule with n = 8 to estimate the area of the pool. (Round your answer to the nearest square meter.) Need Help