(a) Find the approximations T10, M10, and S10 for 2 sin x dx. (Round your answers to six decimal places.) T103.967047 M104.016497 S104.000219 Find the corresponding errors ET, EM, and Es. (Round your answers to six decimal places.) ET = 0.051677 EM=0.025839 Es=13.999830 (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| |Esl (c) How large do we have to choose n so that the approximations Tn, Mn, and S, to the integral in part (a) are accurate to within 0.00001? n = n = n = for Tn for Mn for Sn