Find the approximations t10 m10 and s10 for 0intpi 38 sinx

Question

a) Find the approximations T₁₀, M_10, and S₁₀ for ₀∫^π 38 sin x dx. (Round your answers to six decimal places.)

Find the corresponding errors E_T, E_M, and E_S. (Round your answers to six decimal places.)

(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.)

(c) How large do we have to choose n so that the approximations T_n, M_n, and S_n to the integral in part (a) are accurate to within 0.00001?