Integral command doesn't work inside the for loop

Hello. I have this simple code trying to compare analytical solution of few functions with two numerical methods. I used for loop wih the integral command in it but i get many errors.

clear, clc, close all, format long

a = 0;
b = 2;
h1 = b - a;
h2 = (b - a)/2;
n = 1:5;

fprintf('\tAnalytical\tTrapezoid\tSimpson\n\n')

	Analytical	Trapezoid	Simpson

for i = 1:length(n)
    f = @(x) x.^n;
    I = integral(f,a,b);
    Trap = 0.5*h1*(f(a) + f(b));
    Simp = (h2/3)*(f(a) + 4*f(h2) + f(b));
    fprintf('\t%g\t\t\t\t%g\t\t\t%g\n',I(i),Trap(i),Simp(i))
end

Error using .^
Arrays have incompatible sizes for this operation.

Error in solution>@(x)x.^n (line 12)
f = @(x) x.^n;

Error in integralCalc>iterateScalarValued (line 334)
fx = FUN(t);

Error in integralCalc>vadapt (line 148)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen, ...

Error in integralCalc (line 77)
[q,errbnd] = vadapt(vfunAB,interval, ...

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

f = @(x) exp(x);

Trap = 0.5*h1*(f(a) + f(b));
Simp = (h2/3)*(f(a) + 4*f(h2) + f(b));
fprintf('\t%g\t\t\t%g\t\t%g\n',I,Trap,Simp)

Answer 1

[Walter Roberson]

a = 0;
b = 2;
h1 = b - a;
h2 = (b - a)/2;
n = 1:5;

fprintf('\tAnalytical\tTrapezoid\tSimpson\n\n')

	Analytical	Trapezoid	Simpson

for i = 1:length(n)
    f = @(x) x.^n(i);
    I(i) = integral(f,a,b);
    Trap(i) = 0.5*h1*(f(a) + f(b));
    Simp(i) = (h2/3)*(f(a) + 4*f(h2) + f(b));
    fprintf('\t%g\t\t\t\t%g\t\t\t%g\n',I(i),Trap(i),Simp(i))
end

	2				2			2
	2.66667				4			2.66667
	4				8			4
	6.4				16			6.66667
	10.6667				32			12

f = @(x) exp(x);

Trap = 0.5*h1*(f(a) + f(b));
Simp = (h2/3)*(f(a) + 4*f(h2) + f(b));
fprintf('\t%g\t\t\t%g\t\t%g\n',I,Trap,Simp)

	2			2.66667		4
	6.4			10.6667		8.38906
	6.42073			

However, the final printout is nonsense. You are printing out the vector I from the for i loop, along with the scalars Trap and Simp that you just calculated.

[Left Terry]

@Walter Roberson You are right about the final printout, i was focused on the for loop. Anyway it was in front of my eyes, thanks for your help. I think it's working correctly now

clear, clc, close all, format long

a = 0;
b = 2;
h1 = b - a;
h2 = (b - a)/2;
n = 1:5;

fprintf('\tAnalytical\tTrapezoid\tSimpson\n\n')

	Analytical	Trapezoid	Simpson

for i = 1:length(n)
    f = @(x) x.^(n(i));
    I = integral(f,a,b);
    Trap = 0.5*h1*(f(a) + f(b));
    Simp = (h2/3)*(f(a) + 4*f(h2) + f(b));
    fprintf('\t%.3f\t\t%.3f\t\t%.3f\n',I,Trap,Simp)
end

	2.000		2.000		2.000
	2.667		4.000		2.667
	4.000		8.000		4.000
	6.400		16.000		6.667
	10.667		32.000		12.000

f = @(x) exp(x);
I = integral(f,a,b);
Trap = 0.5*h1*(f(a) + f(b));
Simp = (h2/3)*(f(a) + 4*f(h2) + f(b));
fprintf('\t%.3f\t\t%.3f\t\t%.3f\n',I,Trap,Simp)

	6.389		8.389		6.421