Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error. x/8 T 0 8 sin 4x dx=2
Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error. x/8 T 0 8 sin 4x dx=2
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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![Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors
for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error.
*/8
S
0
8 sin 4x dx = 2
Complete the table below for the Midpoint Rule.
4
8
Midpoint Rule
2.0129
2.0032
Absolute Error
0129
.0032
(Round to four decimal places as needed.)
Complete the table below for the Trapezoid Rule.
4
8
n
n
Trapezoid Rule
Absolute Error
(Round to four decimal places as needed.)
16
2.0008
.0008
16
32
2.0002
.0002
32](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F388d9755-03a2-47a3-9500-2926d4656106%2F0fd4ffa2-6c4a-476f-8ea7-bc7812be70f2%2Fwh9dvdl_processed.png&w=3840&q=75)
Transcribed Image Text:Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors
for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error.
*/8
S
0
8 sin 4x dx = 2
Complete the table below for the Midpoint Rule.
4
8
Midpoint Rule
2.0129
2.0032
Absolute Error
0129
.0032
(Round to four decimal places as needed.)
Complete the table below for the Trapezoid Rule.
4
8
n
n
Trapezoid Rule
Absolute Error
(Round to four decimal places as needed.)
16
2.0008
.0008
16
32
2.0002
.0002
32
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