(a) Use the Trapezoidal Rule, with n = 5, to approximate the integral f 6 cos(4x)dx. T5 (b) The actual value of 6 6 cos(4x)dx = (c) The error involved in the approximation of part (a) is Er = L 6 cos(4x)dx – T5

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Book Problem 18
(a) Use the Trapezoidal Rule, with n = 5, to approximate the integral / 6 cos(4x)dx.
T5 =
(b) The actual value of 6 cos(4x)dx
(c) The error involved in the approximation of part (a) is
Er = [ 6 cos(4x)dx – T5 =
(d) The second derivative f"(x) =
The value of K = max |f"(x)| on the interval [0, 1] =
(e) Find a sharp upper bound for the error in the approximation of part (a) using the
K(b-a)³
Error Bound Formula |E7|<
12n2
(f) Find the smallest number of partitions n so that the approximation T, to the integral
is guaranteed to be accurate to within 0.001.
n =
Transcribed Image Text:Book Problem 18 (a) Use the Trapezoidal Rule, with n = 5, to approximate the integral / 6 cos(4x)dx. T5 = (b) The actual value of 6 cos(4x)dx (c) The error involved in the approximation of part (a) is Er = [ 6 cos(4x)dx – T5 = (d) The second derivative f"(x) = The value of K = max |f"(x)| on the interval [0, 1] = (e) Find a sharp upper bound for the error in the approximation of part (a) using the K(b-a)³ Error Bound Formula |E7|< 12n2 (f) Find the smallest number of partitions n so that the approximation T, to the integral is guaranteed to be accurate to within 0.001. n =
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