Implementing a numerical integration expression

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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.

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Answer 1

Roger Stafford 2014-9-8

编辑：Roger Stafford 2014-9-8

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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.

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Wayne 2014-9-8

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 2014-9-8

在 MATLAB Online 中打开

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

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