i am getting error when put definite integral of a ratio whose nemerator & denominator both are definte integral with variable limits.

syms x u
lmf = @(x) exp(-x.^2);
umf = @(x) exp(-(x-5).^2);
h = @(u) exp(-u.^2);
inner_intgrl_1 = int(u.*h,[lmf umf]);
inner_intgrl_2 = int(h,[lmf umf]);
inner_intgrl_3 = inner_intgrl_1./inner_intgrl_2;
outer_intgrl_1 = integral(x.*inner_intgrl_3,x,[0 10]);
outer_intgrl_2 = integral(inner_intgrl_3,x,[0 10]);
c_jb = outer_intgrl_1/outer_intgrl_2

Error using horzcat

Nonscalar arrays of function handles are not allowed; use cell arrays instead.

Error in JB_GT2 (line 15)

inner_intgrl_1 = int(u.*h,[lmf umf]);

Answer 1

[Paul]

Hi jagannath,

In the original code, lmf and umf are function handles (having nothing to do with the sym variable x), and function handles can't be concatenated into an ordinary array. Also, in the call to int the upper and lower bounds are separate, not in an array.

syms x u
lmf = exp(-x.^2);
umf = exp(-(x-5).^2);
h = exp(-u.^2);
inner_intgrl_1 = int(u*h,u,lmf,umf) % specify the variable of integration

inner_intgrl_1 = 

inner_intgrl_2 = int(h,u,lmf,umf)

inner_intgrl_2 = 

inner_intgrl_3 = inner_intgrl_1./inner_intgrl_2

inner_intgrl_3 = 

●

%outer_intgrl_1 = integral(x.*inner_intgrl_3,x,[0 10]);
outer_intgrl_1 = int(x*inner_intgrl_3,x,0,10)  

outer_intgrl_1 = 

outer_intgrl_2 = int(inner_intgrl_3,x,0,10)

outer_intgrl_2 = 

c_jb = outer_intgrl_1/outer_intgrl_2

c_jb = 

Since a closed form solution isn't found:

vpa(c_jb)

ans = 

3.5291408653452511935031254476839

[jagannath]

No, i found the problem lately. Actually in the outer integration it was not allowed to integrate arrays. Though thanks for reply