How can I compute the following triple integral for a function handle that is expressed by x(1), x(2), x(3)?

I am trying to solve the following triple integral but I get an error message.

I could use x(1)=x, x(2)=y, x(3)=z, but I want to express [x,y,z] as x=[x(1),x(2),x(3)]. Any idea?

t = 15;
f = @(x) ( x(1)*(t - x(2))^x(3) ).*(x(2) <= t); 
f_int = integral3(@(x) f(x), 0, Inf, 0, Inf, 0, Inf) 

Answer 1

[Steven Lord]

integral3 requires the function handle you pass in as the first input to accept three input arrays and return an output array of the same size. Your f function assumes that x is a vector with 3 elements which is incompatible with that requirement. One way to resolve this incompatibility is to use arrayfun. But that uncovers a different problem:

t = 15;
f = @(x) ( x(1)*(t - x(2))^x(3) ).*(x(2) <= t); 
newF = @(x, y, z) arrayfun(@(x, y, z) f([x, y, z]), x, y, z);
f_int = integral3(newF, 0, Inf, 0, Inf, 0, Inf) 

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

f_int = NaN

Rather than including (x(2) <= t) in the integrand, why not change the limits of integration? This doesn't avoid the NaN issue but does make the integrand simpler to debug.

t = 15;
g = @(x) ( x(1)*(t - x(2))^x(3) ); 
newG = @(x, y, z) arrayfun(@(x, y, z) g([x, y, z]), x, y, z);
f_int = integral3(newG, 0, Inf, 0, t, 0, Inf) 

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

f_int = NaN

At some point your integrand boils down to 0*Inf I believe. You will need to determine how to handle that.