Implementing a numerical integration expression

Hi All

I am struggling to implement the following expression in Matlab. The expression seems fairly straight forward, but I just can't get it to run. Any help would be appreciated.

 Thanks.

Answer 1

[Roger Stafford]

Use matlab's 'integral2' function. It provides for inner integration limits to be functions of the outer variable of integration, which is what you have. Your limits, beta*r1 and beta*r2, depend on beta, the outer variable of integration.

[Wayne]

Thank for the response. Previously, I had done what you said in a similar way. Using that approach I had managed to get a solution, but when I try to modify the 1/beta^3 term to a different case of interest, i.e. 1/beta^5, a different problem arises. The result goes from a numerical value to NaN. See attached.

%WORKS clear all

r1=1; r2=2;

fun1 = @(x) x.*besselj(1,x)

fun2 = @(beta) (beta.^-3).*integral(fun1,beta.*r1,beta.*r2,'ArrayValued',true)

Z = integral(fun2,0,5,'ArrayValued',true)

%DOES NOT WORK clear all

r1=1; r2=2;

fun1 = @(x) x.*besselj(1,x)

fun2 = @(beta) (beta.^-4).*integral(fun1,beta.*r1,beta.*r2,'ArrayValued',true)

Z = integral(fun2,0,5,'ArrayValued',true) if true % code end

[Roger Stafford]

My advice was to call on 'integral2', not 'integral'. It is specially designed for double integrals, which is what you are dealing with. Read its documentation carefully before trying to use it:

   http://www.mathworks.com/help/matlab/ref/integral2.html