If f has a continuous second derivative on [a, b], then the error E in approximating [ºf IEI ≤ (ba) 127² [max f(x)], a ≤ x ≤ b. Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating f(x) dx by the Trapezoidal Rule is LEI S (b) Simpson's Rule n = fºre (b-a)5 1804 [max (x)], a ≤ x ≤ 6. Use these to find the minimum integer such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule. B'vx+zax √x +2 dx (a) Trapezoidal Rule f(x) dx by Simpson's Rule is 11/07/2023 07:02
If f has a continuous second derivative on [a, b], then the error E in approximating [ºf IEI ≤ (ba) 127² [max f(x)], a ≤ x ≤ b. Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating f(x) dx by the Trapezoidal Rule is LEI S (b) Simpson's Rule n = fºre (b-a)5 1804 [max (x)], a ≤ x ≤ 6. Use these to find the minimum integer such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule. B'vx+zax √x +2 dx (a) Trapezoidal Rule f(x) dx by Simpson's Rule is 11/07/2023 07:02
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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![If f has a continuous second derivative on [a, b], then the error E in approximating [ºf
IEI ≤ (ba)
127² [max f(x)], a ≤ x ≤ b.
Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating
f(x) dx by the Trapezoidal Rule is
LEI S
(b) Simpson's Rule
n =
fºre
(b-a)5
1804
[max
(x)], a ≤ x ≤ 6.
Use these to find the minimum integer such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule.
B'vx+zax
√x +2 dx
(a) Trapezoidal Rule
f(x) dx by Simpson's Rule is
11/07/2023 07:02](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff585c19b-ef83-4b9a-93dd-0cb9fc8d5f5b%2Ff71b5b46-c732-4009-b7fe-0d7af5c39dae%2Fbejy4hdc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If f has a continuous second derivative on [a, b], then the error E in approximating [ºf
IEI ≤ (ba)
127² [max f(x)], a ≤ x ≤ b.
Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating
f(x) dx by the Trapezoidal Rule is
LEI S
(b) Simpson's Rule
n =
fºre
(b-a)5
1804
[max
(x)], a ≤ x ≤ 6.
Use these to find the minimum integer such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule.
B'vx+zax
√x +2 dx
(a) Trapezoidal Rule
f(x) dx by Simpson's Rule is
11/07/2023 07:02
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