Consider the error formulas. IES 2² max IF"(x)], asxsb IEI ≤ (b-a)³ [max [f(4)(x)|], as xsb 1800 Simpson's Rule Use these to estimate the errors in approximating the integral, with n= 4, using the Trapezoidal Rule and Simpson's Rule. 1²(x² + (a) Trapezoidal Rule (x²+2x) dx (b) Simpson's Rule Trapezoidal Rule Need Help? Read It r

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Consider the error formulas.
IEI ≤ (b-a)³
12n²
(b-a)5₁
180n4
-[max [f"(x)], a ≤ x ≤ b
[max [f(4)(x)], a ≤x≤ b
Simpson's Rule
Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule.
[²₁x²
(a) Trapezoidal Rule
E S
(x² + 2x) dx
(b) Simpson's Rule
Need Help? Read It
Trapezoidal Rule
r
ר
Transcribed Image Text:Consider the error formulas. IEI ≤ (b-a)³ 12n² (b-a)5₁ 180n4 -[max [f"(x)], a ≤ x ≤ b [max [f(4)(x)], a ≤x≤ b Simpson's Rule Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule. [²₁x² (a) Trapezoidal Rule E S (x² + 2x) dx (b) Simpson's Rule Need Help? Read It Trapezoidal Rule r ר
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