integral definite, what is the code to implement it?

I have to imlement this integral...help.

[darova]

What have you done already? What about analytical solution

[Antonino Alesci]

omega: is a vector (1x229)

Omega is a number

[darova]

What are you trying to say?

Answer 1

[Basil C.]

syms r
expr= 2*pi*rho*(omega- W/2)*W*r^3;

F = int(expr,a,b) ,it computes the definite integral of expr from a to b.

Answer 2

[Walter Roberson]

Assuming omega is a numeric vector and that an output is to be created for each:

syms pi rho Omega W r R
expr = 2*pi*rho*(Omega- W/2)*W*r^3;
Tn_inf = int(expr, r, 0, R);

all_Tn_inf = subs(Tn_inf, Omega, omega);