Consider the error formulas. (b- a)³₁ 12n² (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. 1 h²₁ (x - 1)²² |E| ≤ |E| ≤ (a) Trapezoidal Rule (b) Simpson's Rule -[\pre{max{ |f"(x)|], a ≤ x ≤ b Trapezoidal Rule -[max f(4)(x)], a ≤x≤ b dx Simpson's Rule
Consider the error formulas. (b- a)³₁ 12n² (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. 1 h²₁ (x - 1)²² |E| ≤ |E| ≤ (a) Trapezoidal Rule (b) Simpson's Rule -[\pre{max{ |f"(x)|], a ≤ x ≤ b Trapezoidal Rule -[max f(4)(x)], a ≤x≤ b dx 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| ≤
(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.
|E| ≤
(b
- a)³ [\pre{max{ [f"(x)\], a≤x≤ b Trapezoidal Rule
12n²
8
1
1)²
(x -
(a) Trapezoidal Rule
(b) Simpson's Rule
-[max [f(4)(x)], a ≤x≤ b
dx
Simpson's Rule](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad6d3305-3f03-4e1d-b5fa-fcc90cc2dc7c%2Ff74ba23c-f95c-45ac-a288-0c5997982ab6%2Fr6461me_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the error formulas.
|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.
|E| ≤
(b
- a)³ [\pre{max{ [f"(x)\], a≤x≤ b Trapezoidal Rule
12n²
8
1
1)²
(x -
(a) Trapezoidal Rule
(b) Simpson's Rule
-[max [f(4)(x)], a ≤x≤ b
dx
Simpson's Rule
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