cosine (x) -1 -0.8 -0.6 -0.4 -0.2 1.2 0.8 0.6 0.4 0.2 -0 0 x (radians) Figure Q4 0.2 0.4 0.6 0.8 a) Using the midpoint rule numerical integration method with 2 equal intervals, determine the area under the graph shown in figure 4. b) Using Simpson's rule with a single interval, determine the area under the graph shown in figure 4. c) Using Gauss integration with 2 integration points, determine the area under the graph shown in figure 4. d) Discuss the relative accuracy of the results calculated in parts (a), (b) and (c), stating the limitations of each method in relation to the problem being solved.
cosine (x) -1 -0.8 -0.6 -0.4 -0.2 1.2 0.8 0.6 0.4 0.2 -0 0 x (radians) Figure Q4 0.2 0.4 0.6 0.8 a) Using the midpoint rule numerical integration method with 2 equal intervals, determine the area under the graph shown in figure 4. b) Using Simpson's rule with a single interval, determine the area under the graph shown in figure 4. c) Using Gauss integration with 2 integration points, determine the area under the graph shown in figure 4. d) Discuss the relative accuracy of the results calculated in parts (a), (b) and (c), stating the limitations of each method in relation to the problem being solved.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Question 4
Transcribed Image Text:cosine (x)
-1
-0.8
-0.6
-0.4
-0.2
1.2
0.8
0.6
0.4
0.2
-0
0
x (radians)
Figure Q4
0.2
0.4
0.6
0.8
a) Using the midpoint rule numerical integration method with 2 equal intervals, determine the
area under the graph shown in figure 4.
b) Using Simpson's rule with a single interval, determine the area under the graph shown in
figure 4.
c) Using Gauss integration with 2 integration points, determine the area under the graph shown
in figure 4.
d) Discuss the relative accuracy of the results calculated in parts (a), (b) and (c), stating the
limitations of each method in relation to the problem being solved.
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