# I need help to execute a triple integral

7 views (last 30 days)
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?

Torsten on 28 Sep 2022
Edited: Torsten on 28 Sep 2022
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 xminxxmax, ymin(x)yymax(x) and zmin(x,y)zzmax(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
Perfect! thank you so much!

Kevin Holly on 28 Sep 2022
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.
OK! thank you!!

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