Is there any way to solve this integration with loop?

r = 1:10

t= 1: 10

Answer 1

[Walter Roberson]

Yes, you could replace the following symsum() with a loop that totaled over m

syms m t r positive
syms r__prime real
Pi = sym(pi)

Pi = 

π

V_r_t = symsum(exp(m*Pi*t)*sin(m*Pi*r)*int(r__prime*sin(m*Pi*r),r__prime,0,1),m,1,10)

V_r_t = 

[Walter Roberson]

This assumes that is a variable that is independent of r rather than being the derivative of r.

[Bajdar Nouredine]

dear @Walter Roberson thank you very much

how can I add loop if I have intervals for both r and t for example

r= [1,10] and

t= [1,10] ?

[Walter Roberson]

syms m t r positive
syms r__prime real
Pi = sym(pi)

Pi = 

π

V_r_t = symsum(exp(m*Pi*t)*sin(m*Pi*r)*int(r__prime*sin(m*Pi*r),r__prime,0,1),m,1,10)

V_r_t = 

r_vec = 1:10;
t_vec = 1:10;
[R,T] = ndgrid(r_vec,t_vec);
V = subs(V_r_t, {r, t}, {R, T})

V = 

Reminder: sin(INTEGER*pi) is 0, and all of the terms of V_r_t have INTEGER*pi*r and all of your r are integer.

[Bajdar Nouredine]

thanks @Walter Roberson