(a) Find the approximations T10, M10, and S10 for int 0- π (21 sin x) dx. 0 (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 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| ≤ |EM| ≤ |ES| ≤ (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 = for Tn n = for Mn n = for Sn