(a) Find the approximations 710, M10, and S10 for 30 sin(x) dx. (Round your answers to six decimal places.) T10 = M10 S10 = Find the corresponding errors ET, EM, and Es. (Round your answers to six decimal places.) ET = EM = Es = (b) Compare the actual errors in part (a) with the error estimates found by using the smallest possible values for K in the theorem about error bounds for trapezoidal and midpoint ru theorem about error bound for Simpson's rule. (Round your answers to six decimal places.) IETI S IEMI S |Esl S (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T, M, and S to the integral in part (a) are accurate to within 0.00001? For T, n = For M, n = For S, n =