a) Find the approximations T10, M10, and S10 for π 33 sin(x) dx. 0 (Round your answers to six decimal places.) T10 = 65.456277 Correct: Your answer is correct. M10 = 66.272197 Correct: Your answer is correct. S10 = 66.003614 Correct: Your answer is correct. Find the corresponding errors ET, EM, and ES. (Round your answers to six decimal places.) ET = 0.543723 Correct: Your answer is correct. EM = -0.272197 Correct: Your answer is correct. ES = -0.003614 Correct: Your answer is correct. (b) Compare the actual errors in part (a) with the error estimates given by the Theorem about Error Bounds for Trapezoidal and Midpoint Rules and the Theorem about Error Bound for Simpson's Rule. (Round your answers to six decimal places.) |ET| ≤ 0.852673 Correct: Your answer is correct. |EM| ≤ 0.426336 Correct: Your answer is correct. |ES| ≤ 0.005610 Correct: Your answer is correct. (c) How large do we have to choose n so that the approximations Tn, Mn, and Sn to the integral in part (a) are accurate to within 0.00001? n = 3170.0748xx17 for Tn n = 2242 Incorrect: Your answer is incorrect. for Mn n = 56 Incorrect: Your answer is incorrect. for Sn