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Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error. x/8 T 0 8 sin 4x dx=2

Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error. x/8 T 0 8 sin 4x dx=2

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.3: Applications Of Systems Of Linear Equations
Problem 13E: Use sin0=0, sin2=1, and sin=0 to estimate sin3.
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Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error. */8 S 0 8 sin 4x dx = 2 Complete the table below for the Midpoint Rule. 4 8 Midpoint Rule 2.0129 2.0032 Absolute Error 0129 .0032 (Round to four decimal places as needed.) Complete the table below for the Trapezoid Rule. 4 8 n n Trapezoid Rule Absolute Error (Round to four decimal places as needed.) 16 2.0008 .0008 16 32 2.0002 .0002 32
Transcribed Image Text:Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error. */8 S 0 8 sin 4x dx = 2 Complete the table below for the Midpoint Rule. 4 8 Midpoint Rule 2.0129 2.0032 Absolute Error 0129 .0032 (Round to four decimal places as needed.) Complete the table below for the Trapezoid Rule. 4 8 n n Trapezoid Rule Absolute Error (Round to four decimal places as needed.) 16 2.0008 .0008 16 32 2.0002 .0002 32
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