Integration using trapz method

I need to integrate the following function using the trapz method in MATLAB and keep getting errors:

here is my code:

d = 30; E0=8.85e-12; c=.1; P=3.14159265;

a = 0; b = 1;
x = a:dx:b;
N = length(x);

f = @(x) ((d)./(4.*p.*E0))*(c./((sqrt(c.^(2)+x.^(2))).^(3));

y = f(x);

S = 0;
for k = 1:N-1
 S = S + 0.5*(y(k+1) + y(k))*(x(k+1) - x(k));
end

S_trap = trapz(x,y);
S_int = integral(f,a,b);

% print results to pdf
fprintf('INTEGRAL #1\n')
fprintf('Matlab''s integral function yields: %.3f\n',S_int);
fprintf('Matlab''s trapezoid function yields: %.3f\n',S_trap);
fprintf('My trapezoid method yields: %.3f\n\n',S);

% plot integrand and print my trapezoid integration value
figure(1); fplot(f,[a,b])
xlabel('x'); ylabel('f(x)')
title([{'Coulombs Law'},...
 'The approximate area using my trapezoid method is: ',...
 num2str(S,6)]);
grid on

Thank you for any help!

Answer 1

[Stephan]

1 missing bracket and you missed to define dx:

d = 30;
E0=8.85e-12;
c=.1;
dx = 0.1;

a = 0; b = 1;
x = a:dx:b;
N = length(x);

f = @(x) ((d)./(4.*pi.*E0))*(c./((sqrt(c.^(2)+x.^(2))).^(3)));

y = f(x);

S = 0;
for k = 1:N-1
 S = S + 0.5*(y(k+1) + y(k))*(x(k+1) - x(k));
end

S_trap = trapz(x,y);
S_int = integral(f,a,b);

% print results to pdf
fprintf('INTEGRAL #1\n')
fprintf('Matlab''s integral function yields: %.3f\n',S_int);
fprintf('Matlab''s trapezoid function yields: %.3f\n',S_trap);
fprintf('My trapezoid method yields: %.3f\n\n',S);

% plot integrand and print my trapezoid integration value
figure(1); fplot(f,[a,b])
xlabel('x'); ylabel('f(x)')
title([{'Coulombs Law'},...
 'The approximate area using my trapezoid method is: ',...
 num2str(S,6)]);
grid on