Please write a VBA program for 1b and for 2. I am lost. Thank you.
SOLUTION
program integration ! declaring the variable values real results,simp13_res,simp38_res,a,b,error real f integer n external f results=0.0 n=0 a=0.0 b=1.0 error=0.0 write(*,*)achar(10),achar(10) write(*,*)"Intergration of (x^n*e^(x-1)) by dx range of 0 to 1" 10 write(*,*)achar(10) write(*,*)"Enter 0 to exit from the program" write(*,*)"Enter n : " read(*,'(i10)')n !to exit if(n==0)then goto 20 end if !factorial function calling results=factorial(n) !calling the function factorial write(*,*)achar(10),"Recursion Solution = ",results ! print the value of the function !get simpson 1/3 solution call simpson13(f,a,b,simp13_res,real(n)) write(*,*)achar(10),"Simpson 1/3 Solution= ",simp13_res error=(results-simp13_res)*100/results write(*,*)"Relative True Error in Simpson 1/3 (%) = ",abs(error) error=0.0 !get simpson 3/8 solution call simpson38(f,a,b,simp38_res,real(n)) write(*,*)achar(10),"Simpson 3/8 Solution = ",simp38_res error=(results-simp38_res)*100/results write(*,*)"Relative True Error in Simpson 3/8 (%) = ",abs(error) !continue goto 10 20 continue end program integration ! end of the main program, functions are below which is used in this program !recursive algorithm recursive function factorial(n) result(results) real results,first,x integer n x=1 first=1/exp(x) if(n<=0) then results = 0 return else if(n==1) then results=1/exp(x) return else results=1-n*factorial(n-1) return end if end function factorial !simpson 1/3 algorithm Subroutine simpson13(f,a,b,simp38_res,n) real a,b,x,n,h,f,simp38_res h=(b-a)/2.0 simp38_res=h*(f(a,n)+f(a+h,n)+f(b,n))/3.0 return end Subroutine simpson13 !simpson 3/8 algorithm Subroutine simpson38(f,a,b,simp13_res,n) real a,b,x,n,h,f,simp13_res h=(b-a)/3.0 simp13_res=h*3.0*(f(a,n)+3.0*f(a+h,n)+3.0*f(a+2*h,n)+f(b,n))/8.0 return end Subroutine simpson38 !function to integrate function f(x,n) result(res) real x,n,res res=(x**n)*exp(x-1) return end function f
Numerically integrate the below integral doubling the number of intervals until the relative true...
Question 1: Numerically integrate function f(x) given on the right from x=0 to x=10. Use the f(x)= x2 - 6x + 16 Trapezoidal Rule and the Simpson's 1/3 Rule and compare the results. Use at least 4 50 + 15x - ye? decimal digits in your calculations and reporting. Organize and report each one of your solutions in a calculation table and identify your result clearly. a) Divide the interval into 5 subdivisions. Calculate the integral first using the Trapezoidal...
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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...
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...
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.
2. Use the Trapezoidal Rule to numerically integrate the following polynomial from a tob 1.5 f(x) = 0.2 + 25x-200x' + 675xs_ 900x. + 400x5 Use three different numbers of segments (n- 2, n 3, and n 4) and show the effect of the number of segments on relative error considering the exact value of the integral which is 48.7719. (Note: Show the steps of calculation).
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.
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 ×...
Use Matlab code Consider the following function sin(x) Using the following parameters in your functions: -func: the function/equation that you are required to integrate -a, b: the integration limits n: the number of points to be used for the integration I:Integral estimate a) Write a function capable of performing numerical integration of h(x) using the composite trapezoidal rule. Use your function to integration the equation with 9 points. Write a function capable of performing numerical integration of h(x) using the...
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