Plot of a numerical integration

Please someone can help how to plot the following numerical

integration with respect to "z". Here "z" varies from "0" to "1". The

integral need to be done by numerical integration method.

Answer 1

[Star Strider]

Try this:

zv = linspace(0, 1);
for k = 1:numel(zv)
    z = zv(k);
    u_int(k) = integral(@(u) sqrt(u)/((exp(u)/z)-1) + z/(1-z), 0, Inf, 'ArrayValued',1);
end

figure
semilogy(zv, u_int)
grid
xlabel('z')
ylabel('Integrated Value')

.

[P Rakesh Kumar Dora]

Thanks. Here can we change the step size of "z" in your code?

[Star Strider]

It can be whatever you want. This plots 100 points, so the step size is about 0.01. If you want more or fewer, use the third argument to linspace to define how many.

Example —

zv = linspace(0, 1, 20);

creates ‘zv’ as a 20-element vector and would result in a step size of about 0.05. The number of elements can be anything the computer memory permits.

[P Rakesh Kumar Dora]

Ok, Thanks. Do you know how to do this in mathmaticae.Actually i am trying by using

"Nintegrate" function in mathematica , but unable to get the final answer.

[Star Strider]

My pleasure!

I do not have Mathematica and have no experience with it. MATLAB does essentially everything I need to do.

If my Answer helped you solve your problem, please Accept it!

.

[P Rakesh Kumar Dora]

Please can you tell how to locate precise value of the integrand corresponding

to precise value of "z" in the plot?

[Star Strider]

The ‘z’ values are the elements of the ‘zv’ vector. They correspond to the elements of ‘u_int’. So ‘z=0’ corresponds to ‘u_int(1)’, ‘z=1’ to ‘u_int(end)’, with end depending on how many elements of ‘u_int’ you choose to calculate.