Trying to make a loop for a definite integral

I am trying to create a loop for the following definite integral for y=0 to y=20 with step 0.01 in order to make a plot.any ideas are welcome

Answer 1

[Greig]

Is something like this what you are after?

clear vars *;

% Define the function - Note I simplify the denominator in the last term
% Double check the numbers are typed correctly!
F =@(x) 2.906663106 .* x .* ( 1 ./(1 + 1.38 .* x.^4)).^0.4311594203...
 - ( (3.458929096 .* x.^5) ./ (1 + 1.38 .* x.^4).^1.4311594203 );

% define teh Y values and the steps
Y = 0:0.01:20;
nSteps = length(Y);

% preallocate the integral values for speed
Ival = NaN(nSteps-1, 1); 

% Do the loop
for ii = 1:nSteps-1

      Ival(ii) = integral(F, Y(ii), Y(ii+1));

end

% Check it all adds up...

% The whole integral
integral(F, 0, 20)

% The sum of the parts
sum(Ival)

% Then add some plotting function here