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QUESTION 5 The integral I= % dar +4 is to be approximated numerically. (a) Find the...
numerical analysis The integral 1 I = da +4 is to be approximated numerically. (a) Find...
numerical analysis
The integral 1 I = da +4 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by 41,4 ?s"(E), a<<<0, 12 is less than 10-5 for the approximation of I. (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are ci = 1, i = 1,2;rı = 0.5773502692, r2 =...
1+4" QUESTION 5 The integral I= is to be approximated numerically. (a) Find the least integer...
1+4" QUESTION 5 The integral I= is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by b-42f"(E), a<<<b, 12 is less than 10-5 for the approximation of I. (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are g =1, i = 1, 2;rı = 0.5773502692, r2 = -0.5773502692) (9) (c) Evaluate...
QUESTION 5 The integral I= = 1 ata de is to be approximated numerically. (a) Find...
QUESTION 5 The integral I= = 1 ata de is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by ban2f"(0), a<<< is less than 10-s for the approximation of I. (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate 1. (Hint: Parameters are g = 1, i = 1, 2;rı = 0.5773502692, r2 = -0.5773502692)...
QUESTION 5 The integral dir 1 +4 is to be approximated numerically. (a) Find the least...
QUESTION 5 The integral dir 1 +4 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by -haf" (E), a<$<b, is less than 10-5 for the approximation of I. 12 (9) (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are g =1, i = 1, 2;rı = 0.5773502692, r2 = -0.5773502692)...
QUESTION 5 The integral 2 1 I= dx x +4 0 is to be approximated numerically....
QUESTION 5 The integral 2 1 I= dx x +4 0 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite Trapezoidal rule, given by -haf" (), a< & <b, 12 is less than 10-5 for the approximation of I. b - a (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are ci = 1, i...
The integral 1 = ['n ta dor is to be approximated numerically. (a) Find the least...
The integral 1 = ['n ta dor is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by b-9h2f"(E), a<$<b, 12 is less than 10-5 for the approximation of I.
(10 marks) Evaluate the integral [*r'e ce-dx; 1. Using Composite Trapezoidal rule with (n=4) 2. Estimate...
(10 marks) Evaluate the integral [*r'e ce-dx; 1. Using Composite Trapezoidal rule with (n=4) 2. Estimate the error for the approximation in (a) 3. Using Composite 1/3 Simpson's Rule (n = 4).
Objective The usual procedure for evaluating a definite integral is to find the antiderivative of the...
Objective The usual procedure for evaluating a definite integral is to find the antiderivative of the integrand and apply the Fundamental Theorem of Calculus. However, if an antiderivative of the integrand cannot be found, then we must settle for a numerical approximation of the integral. The objective of this project is to illustrate the Trapezoidal Rule and Simpson's Rule. Description To get started, read the section 8.6 in the text. In this project we will illustrate and compare Riemann sum,...
Question 8: 10 Marks The area of the surface described by zf(x,y) for (r,)e R is given by Find an...
Question 8: 10 Marks The area of the surface described by zf(x,y) for (r,)e R is given by Find an approximation to the area of the surface on the hemisphere r2 + y2 + z2-9,2 the region in the plane described by R-((r, yjo-r 1,0 y I) using: 0 that lies above 8.1 Trapezoidal rule in both directions 8.2 Simpson rule in both directions 8.3 Three-term Gaussian quadrature formulas in both directions 131 131
Question 8: 10 Marks The area...
please answer question 5. question 4 is provided for reference. Problem 5: Application of composite integration...
please answer question 5. question 4 is provided for reference.
Problem 5: Application of composite integration rules Assume that you want to approximate the integral of a function in [0, 21 and have only the values of f on specific x values, given in the following table. x005 11.5| 2 (a) Find an approximation to f(x) dx using the composite trapezoid integration rule. Specify all parameters of the approximation and carry out the calculation completely. Assignment 8 MATH363, Spring 2019...
numerical analysis
The integral 1 I = da +4 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by 41,4 ?s"(E), a<<<0, 12 is less than 10-5 for the approximation of I. (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are ci = 1, i = 1,2;rı = 0.5773502692, r2 =...
1+4" QUESTION 5 The integral I= is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by b-42f"(E), a<<<b, 12 is less than 10-5 for the approximation of I. (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are g =1, i = 1, 2;rı = 0.5773502692, r2 = -0.5773502692) (9) (c) Evaluate...
QUESTION 5 The integral I= = 1 ata de is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by ban2f"(0), a<<< is less than 10-s for the approximation of I. (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate 1. (Hint: Parameters are g = 1, i = 1, 2;rı = 0.5773502692, r2 = -0.5773502692)...
QUESTION 5 The integral dir 1 +4 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by -haf" (E), a<$<b, is less than 10-5 for the approximation of I. 12 (9) (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are g =1, i = 1, 2;rı = 0.5773502692, r2 = -0.5773502692)...
QUESTION 5 The integral 2 1 I= dx x +4 0 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite Trapezoidal rule, given by -haf" (), a< & <b, 12 is less than 10-5 for the approximation of I. b - a (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are ci = 1, i...
The integral 1 = ['n ta dor is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by b-9h2f"(E), a<$<b, 12 is less than 10-5 for the approximation of I.
(10 marks) Evaluate the integral [*r'e ce-dx; 1. Using Composite Trapezoidal rule with (n=4) 2. Estimate the error for the approximation in (a) 3. Using Composite 1/3 Simpson's Rule (n = 4).
Objective The usual procedure for evaluating a definite integral is to find the antiderivative of the integrand and apply the Fundamental Theorem of Calculus. However, if an antiderivative of the integrand cannot be found, then we must settle for a numerical approximation of the integral. The objective of this project is to illustrate the Trapezoidal Rule and Simpson's Rule. Description To get started, read the section 8.6 in the text. In this project we will illustrate and compare Riemann sum,...
Question 8: 10 Marks The area of the surface described by zf(x,y) for (r,)e R is given by Find an approximation to the area of the surface on the hemisphere r2 + y2 + z2-9,2 the region in the plane described by R-((r, yjo-r 1,0 y I) using: 0 that lies above 8.1 Trapezoidal rule in both directions 8.2 Simpson rule in both directions 8.3 Three-term Gaussian quadrature formulas in both directions 131 131
Question 8: 10 Marks The area...
please answer question 5. question 4 is provided for reference.
Problem 5: Application of composite integration rules Assume that you want to approximate the integral of a function in [0, 21 and have only the values of f on specific x values, given in the following table. x005 11.5| 2 (a) Find an approximation to f(x) dx using the composite trapezoid integration rule. Specify all parameters of the approximation and carry out the calculation completely. Assignment 8 MATH363, Spring 2019...
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