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A unit circle (radius equal to 1) is expressed by the equation x² + y² = 1 and therefore its area is equal to , see Fig.2. The area of the half circle can be defined as follows: x² + y² =1⇒y=√√1-x² İ√₁-x²dx= -1 Use the following methods to evaluate the integral: (a) Composite Simpson's 1/3 method (use 8 subintervals) (b) Composite Simpson's 3/8 method (use 9 subintervals) (c) Second order (n=2) Gauss quadrature Anc - = T =/2 2

A unit circle (radius equal to 1) is expressed by the equation x² + y² = 1 and therefore its area is equal to , see Fig.2. The area of the half circle can be defined as follows: x² + y² =1⇒y=√√1-x² İ√₁-x²dx= -1 Use the following methods to evaluate the integral: (a) Composite Simpson's 1/3 method (use 8 subintervals) (b) Composite Simpson's 3/8 method (use 9 subintervals) (c) Second order (n=2) Gauss quadrature Anc - = T =/2 2

Advanced Engineering Mathematics
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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A unit circle (radius equal to 1) is expressed by the equation x² + y² = 1 and therefore its area is equal to , see Fig.2. The area of the half circle can be defined as follows: x² + y² = l<y=√√√1-x² Anc π = √ √₁-x²³dx = ²1/² = 2 -1 2 Use the following methods to evaluate the integral: (a) Composite Simpson's 1/3 method (use 8 subintervals) (b) Composite Simpson's 3/8 method (use 9 subintervals) (c) Second order (n=2) Gauss quadrature Write MatLab scripts to derive the results, compare and discuss them
Transcribed Image Text:A unit circle (radius equal to 1) is expressed by the equation x² + y² = 1 and therefore its area is equal to , see Fig.2. The area of the half circle can be defined as follows: x² + y² = l<y=√√√1-x² Anc π = √ √₁-x²³dx = ²1/² = 2 -1 2 Use the following methods to evaluate the integral: (a) Composite Simpson's 1/3 method (use 8 subintervals) (b) Composite Simpson's 3/8 method (use 9 subintervals) (c) Second order (n=2) Gauss quadrature Write MatLab scripts to derive the results, compare and discuss them
-1.4 +1 -1.2 -1 -0.8 -0.6 -0.4 -0.2 1.2 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1.2 Y 1 √1-2² 1 0.2 0.4 0.6 Figure 2: Unit circle 0.8 1.2 1.4 X
Transcribed Image Text:-1.4 +1 -1.2 -1 -0.8 -0.6 -0.4 -0.2 1.2 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1.2 Y 1 √1-2² 1 0.2 0.4 0.6 Figure 2: Unit circle 0.8 1.2 1.4 X
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