(a) Consider the task of approximating e* dr using the Composite Trape- zoidal rule. How large should n and h be chosen in order to ensure that the error is at most 0.0001?
(a) Consider the task of approximating e* dr using the Composite Trape- zoidal rule. How large should n and h be chosen in order to ensure that the error is at most 0.0001?
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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2 a
![(a) Consider the task of approximating / e
zoidal rule. How large should n and h be chosen in order to ensure that the
dx using the Composite Trape-
error is at most 0.0001?
(b) The composite trapezoidal rule is used to approximate the integral
I =
x(x + a*)dx.
i. Complete the table below leaving all your solutions correct to four decimal
places.
1.2
1.25 1.4 1.5 1.6 1.75 1.8 2
B
C
1
f(r.) A 3.8016
D
E
F
G H
ii. Using the data in the table in part (i), apply the composite trapezoidal rule
to find the approximate value of I on [1, 2] with h = 0.25.
T/4
(c) Find the approximate value of the integral I = er sin(2x) dr using Gaus-
sian quadrature with n = 2, the nodes ti = -0.577, t2 = 0.577 and coefficients
1. All your solutions should be expressed correct to three decimal
Ci = C2
points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F650cc1de-9b19-44c4-87ad-8f16a4708575%2F0c23fbac-c821-4ec0-b558-8f9f1caa376b%2Fnxc97dn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Consider the task of approximating / e
zoidal rule. How large should n and h be chosen in order to ensure that the
dx using the Composite Trape-
error is at most 0.0001?
(b) The composite trapezoidal rule is used to approximate the integral
I =
x(x + a*)dx.
i. Complete the table below leaving all your solutions correct to four decimal
places.
1.2
1.25 1.4 1.5 1.6 1.75 1.8 2
B
C
1
f(r.) A 3.8016
D
E
F
G H
ii. Using the data in the table in part (i), apply the composite trapezoidal rule
to find the approximate value of I on [1, 2] with h = 0.25.
T/4
(c) Find the approximate value of the integral I = er sin(2x) dr using Gaus-
sian quadrature with n = 2, the nodes ti = -0.577, t2 = 0.577 and coefficients
1. All your solutions should be expressed correct to three decimal
Ci = C2
points.
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