Question 4 Figure Q4 shows the cosine function between limits of -1 and 1 radians. cosine (x) -1 -0.8 -0.6 -0.4 -0.2 1.2 0.8 0.6 0.4 0.2 0 0 0.2 x (radians) Figure Q4 0.4 0.6 0.8 1 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.
Question 4 Figure Q4 shows the cosine function between limits of -1 and 1 radians. cosine (x) -1 -0.8 -0.6 -0.4 -0.2 1.2 0.8 0.6 0.4 0.2 0 0 0.2 x (radians) Figure Q4 0.4 0.6 0.8 1 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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 64E
Related questions
Question
Q4
Transcribed Image Text:Question 4
Figure Q4 shows the cosine function between limits of -1 and 1 radians.
cosine (x)
-1
-0.8
-0.6
-0.4
-0.2
1.2
0.8
0.6
0.4
0.2
0
0
0.2
x (radians)
Figure Q4
0.4
0.6
0.8
1
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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