error : Function integration trapezoidal

i want to calculate area from numerical integration of function f(x) with the limits a to b and vary n . by the way i use this code from my handbook, numerical chapra. to solve my problem. but the result was error.

function I = trap(func,a,b,n,varargin)
% trap: composite trapezoidal rule quadrature
%   I = trap(func,a,b,n,p1,p2,...):
%                  composite trapezoidal rule
% input:
%   func = name of function to be integrated
%   a, b = integration limits
%   n = number of segments (default = 100)
%   p1,p2,... = additional parameters used by func
% output:
%   I = integral estimate

if nargin<3,error('at least 3 input arguments required'),end
if ~(b>a),error('upper bound must be greater than lower'),end
if nargin<4|isempty(n),n=100;end
x = a; h = (b - a)/n;
s=func(a,varargin{:});
for i = 1 : n-1
  x = x + h;
  s = s + 2*func(x,varargin{:});
end
s = s + func(b,varargin{:});
I = (b - a) * s/(2*n);

the error :

??? function I = trap(func,a,b,n,varargin)
    |
Error: Function definitions are not permitted in this context.

what should i do ?

--- my purpose is to make the table like below this text, to known how the error result with vary n parameter.

%

[sixwwwwww]

you can't directly run this function. first save it in an m-file with name 'trap.m' and then call with appropriate input parameters from command prompt or from another script

[jakv]

what the script that i can use ? sorry i'm newbie.

Answer 1

[sixwwwwww]

Maybe following links are helpful for you for this purpose:

http://www.youtube.com/watch?v=qo3AtBoyBdM

http://www.youtube.com/watch?v=AzvOc5odmDg

These links shows how to use matlab functions. and how to input and get output values from them

[jakv]

thanks, i could used the script correctly,

i still confuse about this script

if nargin<3,error('at least 3 input arguments required'),end
if ~(b>a),error('upper bound must be greater than lower'),end
if nargin<4|isempty(n),n=100;end

especially nargin and varargin.

what the means of above script ?

[sixwwwwww]

'varargin' mean variable number of input arguments and 'nargin' mean number of input arguments. If you use 'varargin' in function definition then you can input any number of arguments to that function and by using 'nargin' you can know how many arguments are input to a function. For more information see:

http://www.mathworks.com/help/matlab/ref/varargin.html

http://www.mathworks.com/help/matlab/ref/nargin.html

Good luck!

[Ahzabuddin]

can you help me too??? I get trapezoidal single... but I have trouble unequal trapezoidal.

x = [0 .12 .22 .32 .36 .4 .44 .54 .64 .7 .8];

y = 0.2+25*x-200*x.^2+675*x.^3-900*x.^4+400*x.^5;

>>trapuneq(x,y)

??? Undefined function or variable 'l'.

Error in ==> trapuneq at 18

s = s+(x(k+l)-x(k))*(y(k)+y(k+l))/2;

my formula M-File is

if nargin<2,error('at least 2 input arguments required'),end

if any(diff(x)<0),error('x not monotonically ascending'),end

n = length(x);

if length(y)~=n,error('x and y must be same length'); end

s = 0;

for k = 1:n-1

s = s+(x(k+l)-x(k))*(y(k)+y(k+l))/2;

end

I = s;

[Sam]

Changing the 2 "l"s ("L"s; Capital shown for variable clarity) to a "1" ("One") in the line of the For loop fixes the error and allows the same anser to be attained as shown in the textbook (1.5948).

Answer 2

[Torsten]

My guess is that the "l" in the formula

s = s+(x(k+l)-x(k))*(y(k)+y(k+l))/2;

should be a "1".

Best wishes

Torsten.

[Sam]

Yes this appears to be correct, @Torsten.