(10 marks) Evaluate the integral [*r'e ce-dx; 1. Using Composite Trapezoidal rule with (n=4) 2. Estimate...
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...
2- Evaluate the following integral: 0.4 | Vcos(2x)dx a) By calculator, b) Composite trapezoidal rule (with segment no. n=4) and determine the true relative error, c) Composite Simpson's 1/3 with n =4 and determine the true relative error, d) Simpson's 3/8 rule determine the true relative error, e) Composite Simpson's rule, with n =5, determine the true relative error.
4. For: 1 + x3 dx a) Evaluate I using the trapezoidal rule with n= 4. (15 pts) b) Evaluate I using the 1/3 Simpson's rule with n=2. (10 pts) Trapezoidal Rule Single Application 1 = (6-a) f(b) + f(a) Composite (b-a) 2n I= i=1 Simpson's 1/3 Rule Single Application Composite b) Evaluate I using the 1/3 Simpson's rule with n=2. (10 pts) Trapezoidal Rule Single Application f(b) + f(a) I = (b-a) 2 Composite I = (b − a)...
2. The following integral 2 dr can be computed exactly (a) Estimate the integral using the composite trapezoidal rule with n = exact value of integral and compute the true percent relative error for this approximation 4. Calculate the (b) How many subintervals would be needed to estimate the integral with the composite trapezoidal rule with an accuracy of 102? (c) Estimate the integral using the composite Simpson's 1/3 rule with n = true percent relative error for this approximation...
4. Find the exact value of the integral. Then use composite trapezoidal rule and the composite Simpson's rule to approximate the integral below using n 4 and n 8. Round your results to four decimal places. .3 2a +3a2 dx
2 Problem 3 (25 points) Let I = ïrdz. a) [by hand] Use a composite trapezoidal rule to evaluate 1 using N = 3 subintervals. b) MATLAB] Use a composite trapezoidal rule to evaluate I using N - 6 subinterval:s c) by hand] Use Romberg extrapolation to combine your results from a) and b) and obtain an improved approximation (you may want to compare with a numerical approximation of the exact value of the integral 2 Problem 3 (25 points)...
4. This question is about using the composite Simpson's Rule to estimate the integral 1 = (exp() dr to ten decimal places. (a) Enter and save the following Matlab function function y = f(x) y =exp(x/2); end [O marks) (b) Now complete the following Matlab function function y = compSR (a,b,N) end The function is to return the estimate of I found by applying Simpson's Rule N times. The Matlab function from the previous part of the question should be...
(a) Estimate So sin(x + 1) dx by using either Simpson's Rule or Trapezoidal Rule with n= 6 (Round the answer to 6 decimal places). (b) Estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than 10-4 by the rule you used in part (a).
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?
Evaluate Integral from 2 to 10 StartFraction 9 Over s squared EndFraction ds using the trapezoidal rule and Simpson's rule. Determine Evaluate ds using the trapezoidal rule and Simpson's rule. Determine The value of (Round to four decimal places as needed.) i. the value of the integral directly. ii. the trapezoidal rule estimate for n = 4. iii. an upper bound for ET iv: the upper bound for Et as a percentage of the integral's true value. v. the Simpson's...