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(a) Find the approximations T10, M10, and S10 for 9 sin(x) dx. (Round your answers to six decimal places.) T10= M10- $10- Find the corresponding errors E, EM, and Es. (Round your answers to six decimal places.) E₁ = EM- Eg= (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.) Eμls Ess (c) 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? n= n= for T for Me

(a) Find the approximations T10, M10, and S10 for 9 sin(x) dx. (Round your answers to six decimal places.) T10= M10- $10- Find the corresponding errors E, EM, and Es. (Round your answers to six decimal places.) E₁ = EM- Eg= (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.) Eμls Ess (c) 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? n= n= for T for Me

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Find the approximations T10, M10, and S10 for 9 sin(x) dx. (Round your answers to six decimal places.) T10= M10- $10- Find the corresponding errors E, EM, and Es. (Round your answers to six decimal places.) E₁ = EM- Eg= (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.) Eμls Ess (c) 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? n= n= for T for Me
Transcribed Image Text:(a) Find the approximations T10, M10, and S10 for 9 sin(x) dx. (Round your answers to six decimal places.) T10= M10- $10- Find the corresponding errors E, EM, and Es. (Round your answers to six decimal places.) E₁ = EM- Eg= (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.) Eμls Ess (c) 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? n= n= for T for Me
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