Question

matlab help plz

Overview: In this exercise, you will write code to compare how two different mumerical methods (a middle Riemann sum, and MATLAB's integral function) evaluate the function fx) and the x-axis. The code should output the error between the two calculated areas. area between a Function Inputs Func- the function to be numerically integrated. a-the lower interval value. b-the upper interval value. N-the number of rectangles to be used. Function Outputs: Area Riemann- the numerical approximation for the area under the curve using a middle Riemann sum Area integral-the numerical approximation for the area under the curve using the integral function. Error- the absolute error between the two area calculations (this should always be a positive mumber). Process: Step 1: Solve Area_Riemann - consult your answer from Q3 of last week's exercises. fom Q1 of last week's exercises Step 2: Solve Area_integral -consult your answer Step 3: Solve Error. Useful Functions: 1inspace, sum, abs. Example test When you run your code in MATLAB, it should provide the same answers as when you run the (protected) MATLAB script areal.p. This script file is available Schedule table. Save it into your MATLAB working directory to be able to access the solution function areal from within MATLAB. Eg [Area Riemann, Area integral, Error] areal(@(x) x. 2, e, 1, 10) should return from Bb, Area_Riemann 0.3325, Area_integral e.3333, Error 8.3333e-04. [Area Riemann, Area integral, Error] areal(@(x) x. 2, e, 1, 100) should return Area Riemann 0.3333, Area integral e.3333, Error - 8.3333e-06. Function Template: function [Area Riemann, Area integral, Error] KINSERT CODE end areal (Func, a,, N) could you plz help me with this one in matlab

Answer 1

integrals.m

F e (x) x.^2; SEnter the desired function x0 0 xl 1 N = 100 [Area_R,Area_I,E] = areal (F, x0,xl,N); fprintf'Area_Reimann = %.4f\n',round (Area_R, 4)); fprintf 'Area_Integral = %.4f\n',round (Area_I,4)); fprintf('Error = is\n',sprintf('%.4e\t',E)); 2 %lower limit 3 Supper limit 4 No. of Rectangles 5 6 7 8

F =@(x) x.^2; %Enter the desired function
x0 = 0; %lower limit
x1 = 1; %upper limit
N = 100; %No. of Rectangles
[Area_R,Area_I,E] = area1(F,x0,x1,N);
fprintf('Area_Reimann = %.4f\n',round(Area_R,4));
fprintf('Area_Integral = %.4f\n',round(Area_I,4));
fprintf('Error = %s\n',sprintf('%.4e\t',E));

area1.m

|function [Area_Reimann, Area_integral, Error] h= (b-a)/N Area Reimann-0.0; ci-linspace (a+h/2,b-h/2,N); yFunc (ci) Area_Reimann = h*sum (y); Area_integral = integral (Func,a,b); Error Area_integral - Area_Reimann; = areal (Func, a,b, N) 2 4 5 7 8 end

function [Area_Reimann,Area_integral,Error] = area1(Func,a,b,N)
h=(b-a)/N;
Area_Reimann=0.0;
ci=linspace(a+h/2,b-h/2,N);
y=Func(ci);
Area_Reimann = h*sum(y);
Area_integral = integral(Func,a,b);
Error = Area_integral - Area_Reimann;
end

OUTPUT:

for N=10(Change the value of N in integrals.m):

Area Reimann = 0.3325 Area Integral = 0.3333 Error 8.3333e-04

for N=100

Area Reimann = 0.3333 Area_Integral = 0.3333 Error 8.3333e-06