I need help to execute a triple integral

im trying to do the following:

clear all

clear close

syms s r m;

fun = @(s,m,r)(r.*exp(-(s.^2/2+1.727*(m-5))))./(sqrt(r.^2-10^2));

result= integral3(fun,-inf,-(-1.85-1.013*(m-6)+1.496*log(sqrt(r.^2+31.025))),5,7.5,10,18);

final_result=result*(2*1.727)/(sqrt(2*pi)*30);

BUT matlab say me that in the intregral3 i have a invalid argument at position 3.

What am i doing wrong?

Answer 1

[Torsten]

You still didn't get the point.

Look at the documentation of integral3:

q = integral3(fun,xmin,xmax,ymin,ymax,zmin,zmax) approximates the integral of the function z = fun(x,y,z) over the region xmin ≤ x ≤ xmax, ymin(x) ≤ y ≤ ymax(x) and zmin(x,y) ≤ z ≤ zmax(x,y)

Thus if your integration limit is a function of both other variables, it must appear as the last variable in the list ( in this case s ).

And this limit has to be a function handle, not a simple algebraic (or even symbolic) expression.

s = @(m,r) -(-1.85-1.013*(m-6)+1.496*log(sqrt(r.^2+31.025)));
fun = @(m,r,s)(r.*exp(-(s.^2/2+1.727*(m-5))))./(sqrt(r.^2-10^2));
result= integral3(fun,5,7.5,10,18,-Inf,s);
final_result=result*(2*1.727)/(sqrt(2*pi)*30)

final_result = 0.0154

[Jose Miguel Araya Martinez]

Perfect! thank you so much!

Answer 2

[Kevin Holly]

Your value for xmax needs to be a floating-point array.

syms s r m;
fun = @(s,m,r)(r.*exp(-(s.^2/2+1.727*(m-5))))./(sqrt(r.^2-10^2))

fun = function_handle with value:
    @(s,m,r)(r.*exp(-(s.^2/2+1.727*(m-5))))./(sqrt(r.^2-10^2))

result= integral3(fun,-inf,inf,5,7.5,10,18) % I placed inf for the xmax

result = 21.4335

final_result=result*(2*1.727)/(sqrt(2*pi)*30)

final_result = 0.9845

Here I changed the value of xmax

result= integral3(fun,-inf,30,5,7.5,10,18)

result = 21.4335

result= integral3(fun,-inf,10,5,7.5,10,18)

result = 21.4335

if you place a symbolic, you will get an error as shown below.

result= integral3(fun,-inf,r,5,7.5,10,18)

Error using integral3
Invalid argument at position 3. Value must be a floating-point array.

[Jose Miguel Araya Martinez]

OK! thank you!!