dx % 1 +z? 0 a) b) Evaluate analytically. Write a MATLAB program to numerically integrate the above using the rectangular rule. dx % 1 +z? 0 a) b) Evaluate analytically. Write a MATLAB progr...
USE MATLAB ONLY NEED MATLAB CODE
MATLAB
21.4 Integrate the following function analytically and using the trapezoidal rule, with - 1,2,3, and 4: 0 (x + 2/x dx 0 Use the analytical solution to compute true percent relative crrors to evaluate the accuracy of the trapezoidal approximations. 0
Evaluate the integral integral_0 15^2x dx analytically, using the Trapezoidal Rule (1-segment), and Simpson's 1/3 Rule (1-segment). Then use the Matlab trap() function presented in class to find a solution exact to 4 decimal places. How many segments were required for this accuracy?
3. Evaluate the triple integral below (a) analytically, (b) using the composite trapezoidal rule with n 2, (c) a single application of Simpson's 1/3 rule, and (d) for each approximation, determine the true percent relative error based on (a). 2yz)dx dy dz
3. Evaluate the triple integral below (a) analytically, (b) using the composite trapezoidal rule with n 2, (c) a single application of Simpson's 1/3 rule, and (d) for each approximation, determine the true percent relative error based on...
4.30 Write a MATLAB program that uses implicit Euler to integrate dx Use an initial condition y(0)-1 and integrate until x 2. What equations are needed for Newton's methiod? Is this solution becoming unstable?
1. Use the Trapezoidal Rule to numerically integrate the following polynomial from a = 0.5 to b = 1.5 f(x) = 0.2 + 25x – 200x2 +675x3 – 900x4 + 400x5 Use three different number of segments and show that higher number of segments give lesser relative error considering the exact value of the integral, which is 49.3667. 2. Write a MATLAB or OCTAVE code to solve the above problem numerically and verify your result. Copy/paste the code and answers...
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...
(15 pts Question 6: Evaluate the following integral: 1*(1 – e-x) dx (a) Analytically (b) Single application of the trapezoidal rule (e) Multiple-application trapezoidal rule, with n = 2 and 4
integrate with your best choice
(substitution rule, by parts, or partial fractions)
d) ( z*In(a)dx e) / ** +20 – 12 I x(x2 - 1 dx
3. Evaluate the following double integral (a) analytically. (b) using multiple-application of the trapezoidal rule with n 2 and compute the true relative error. (c) using single application of Simpson's 1/3 rule and compute the true relative erro.
3. Evaluate the following double integral (a) analytically. (b) using multiple-application of the trapezoidal rule with n 2 and compute the true relative error. (c) using single application of Simpson's 1/3 rule and compute the true relative erro.
Please write a VBA program for 1b and for 2. I am lost. Thank
you.
Numerically integrate the below integral doubling the number of intervals until the relative true error falls below 0.01%. Where 1. Using multiple application of the a. Trapezoidal Rule b. Simpson's 1/3 Rule 2. Using Romberg Integration with the Trapezoidal Rule 4 2N 3 3 and a table listing as coluns: number of intervas, approximate integral value, relative true error. That is, for part 1(a) and...