Kindly help me integrate this function.

I am trying to integrate the following expression using 'quad' fuction but MATLAB is giving errors, kindly help me with the code. Code starts below:

f= @(x) ((sin(x))^2)/(((sin(x))^2)+(7));

% a, the lower limit

a= 0 ;

% b, the upper limit

b= pi/2 ;

answer=quad(f,a,b);

%%% Code ends

MATLAB gives following error:

??? Error using ==> mpower Inputs must be a scalar and a square matrix.

Error in ==> @(theta)((sin(theta))^2)/(((sin(theta))^2)+(7))

Error in ==> quad at 77 y = f(x, varargin{:});

Kindly help.

Answer 1

[Star Strider]

You need to vectorize your code.

This works:

f= @(x) ((sin(x)).^2)./(((sin(x)).^2)+(7));
a= 0 ;
b= pi/2 ;
answer=quad(f,a,b);

produces:

answer =

     101.4509e-003

[Furqan Haider]

Bundle of thanks Star Strider, i am facing an other issue. In the function statement, instead of '7' I have a vector h=1:0.02:10 i.e.

f= @(x) ((sin(x)).^2)./(((sin(x)).^2)+(h));

I wish to integrate my function for all the values of vector 'h'. Can u help me out ?

[Star Strider]

My pleasure!

Here is your integral over your vector h:

h=1:0.02:10;

a= 0 ;
b= pi/2 ;

for k1 = 1:length(h)
    H = h(k1);
    f= @(x) ((sin(x)).^2)./(((sin(x)).^2)+H);
    answer(k1)=quad(f,a,b);
end

Your answer variable is now a vector of length(h). When I plotted it, it looked like a smooth decaying exponential.

[Furqan Haider]

Thank u again, I got what was required.

Best regards.

[Star Strider]

My pleasure!