Consider the error formulas. |E| ≤ (b − a)³ [max [f"(x)], a≤x≤ b 12n² |E| ≤ (b-a)5 180n4 Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule. [²₁x². + 9x) dx (a) Trapezoidal Rule X -[max [ƒ(4)(x)|], a ≤x≤ b (b) Simpson's Rule Trapezoidal Rule Simpson's Rule
Consider the error formulas. |E| ≤ (b − a)³ [max [f"(x)], a≤x≤ b 12n² |E| ≤ (b-a)5 180n4 Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule. [²₁x². + 9x) dx (a) Trapezoidal Rule X -[max [ƒ(4)(x)|], a ≤x≤ b (b) Simpson's Rule Trapezoidal Rule Simpson's Rule
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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![Consider the error formulas.
|E| ≤
|E| ≤
(b − a)³
12n²
2
[²0
(b − a) 5
180n4
Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule.
(+2
-[max [f"(x)]], a ≤ x ≤ b
(a) Trapezoidal Rule
X
+ 9x) dx
(b) Simpson's Rule
-[max [ƒ(4)(x)|], a ≤ x ≤ b
Trapezoidal Rule
Simpson's Rule](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb898cad9-5347-4e0a-a74d-32f84bfad0f6%2Fbfb5d677-515b-4d16-ac98-fcd963fd9b11%2F2813zd_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the error formulas.
|E| ≤
|E| ≤
(b − a)³
12n²
2
[²0
(b − a) 5
180n4
Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule.
(+2
-[max [f"(x)]], a ≤ x ≤ b
(a) Trapezoidal Rule
X
+ 9x) dx
(b) Simpson's Rule
-[max [ƒ(4)(x)|], a ≤ x ≤ b
Trapezoidal Rule
Simpson's Rule
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