b:
syms x
fun = exp(-x^2)
a = 0
b = 1
n = 6
result = trap(a, b, n, fun)
result =
0.7451
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 subin...
Let x In I dx. a) Find the exact value of 1 b) Use composite trapezoidal rule with n = 4 subintervals to approximatel. Calculate the exact error c) Use composite simpson's rule with n = 4 subintervals to approximatel. Calculate the d) Use composite simpson's rule with n = 6 subintervals to approximate I. Calculate the exact error exact error
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...
How would you code this on matlab? Wirite a code to find an approximation for the composite trapezoidal rule. dr witiferent mumber of sabintervals using Use the following number of subintervals namely, n 10,n 20,n-40 andn 100 and calculate the global errors in each case. Wirite a code to find an approximation for the composite trapezoidal rule. dr witiferent mumber of sabintervals using Use the following number of subintervals namely, n 10,n 20,n-40 andn 100 and calculate the global errors...
(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).
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
Numerical Methods Consider the integral 2 (a) [16 marks] Use the composite Simpson's rule with four intervals to calculate (by hand) approximate value of the integral Calculate the maximum value of the error in your approximation, and compare it with the true error. (b) 19 marks] Determine the number of subintervals n and the step size h so that the composite Simpson's rule for n subintervals can be used to compute the given integral with an accuracy of 5 ×...
4) (25 pts) Evaluate the integral d: +5 Using the following methods: a) Analytically b) Trapezoidal rule. Divide the whole interval into four subintervals (n 4) c) Simpson's 1/3 rule. Divide the whole interval into four subintervals (n 4). d) Simpson's 3/8 rule. Divide the whole interval into three subintervals (n 3) Compare the results in b), c), and d) with the true value obtained in a). 4) (25 pts) Evaluate the integral d: +5 Using the following methods: a)...
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error bound for 1-Tr. Using the rigorous error n should be in order that li-Tal 3x 10-0 (35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error...
- Sox using with 2,4, and equal o Evaluate the integral i) Composite trapezoidal rub, () composite simpsunds rule sub infortals. y Evaluate the integral Subdividing the interval parts and then applying three pant formula. I=s dx by to, i] into two equal the Gauss Legentre • Ttx i tx 1a) Evaluate the Integral I= ĵ dx using i) Composite trapezoidal ic Composite Simpson rule sub intervals rule si into 2,4 and 8 3) Evaluate the integral I = I...
3. Find the value of V1+r3dr, using the composite trapezoidal rule, to 5 decimal places. How many subintervals do you need to use to attain this accuracy? Make a convergence plot to show that the composite trapezoidal rule is second order in this case 3. Find the value of V1+r3dr, using the composite trapezoidal rule, to 5 decimal places. How many subintervals do you need to use to attain this accuracy? Make a convergence plot to show that the composite...