Problem 4 (a) A table of values of a function g is given. Use Simpson's Rule to estimate fù g(x) dx. x 0.0 0.2 0.4 0.6 0.8 g(x) x 12.1 1.0 11.6 1.2 11.3 1.4 11.1 1.6 12.2 11.7 g(x) 11.2 11.6 12.0 (b) If − 6 ≤ g(4)(x) ≤ 2 for 0 ≤ x ≤ 1.6, estimate the error involved in the approximation in part (a). (c) What is an average value of g(x) on 0 ≤ x ≤ 1.6? (d) How large should we take n in order to guarantee that the Simpson's Rule approximation for 5¹6 g(x) dx would be accurate to within 10-6 ? 1.6
Problem 4 (a) A table of values of a function g is given. Use Simpson's Rule to estimate fù g(x) dx. x 0.0 0.2 0.4 0.6 0.8 g(x) x 12.1 1.0 11.6 1.2 11.3 1.4 11.1 1.6 12.2 11.7 g(x) 11.2 11.6 12.0 (b) If − 6 ≤ g(4)(x) ≤ 2 for 0 ≤ x ≤ 1.6, estimate the error involved in the approximation in part (a). (c) What is an average value of g(x) on 0 ≤ x ≤ 1.6? (d) How large should we take n in order to guarantee that the Simpson's Rule approximation for 5¹6 g(x) dx would be accurate to within 10-6 ? 1.6
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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Transcribed Image Text:Problem 4
(a) A table of values of a function g is given. Use
Simpson's Rule to estimate 6 g(x) dx.
1.6
X
0.0
0.2
0.4
0.6
0.8
g(x)
12.1
11.6
11.3
11.1
11.7
g(x)
1.0
11.2
1.2
11.6
1.4
12.0
1.6 12.2
X
(b) If − 6 ≤ g(x) ≤ 2 for 0 ≤ x ≤ 1.6, estimate the error
involved in the approximation in part (a).
(c) What is an average value of g(x) on 0≤x≤ 1.6?
(d) How large should we take n in order to guarantee that the Simpson's Rule
approximation for ¹6 g(x) dx would be accurate to within 10-6?
-1.6
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