Integration in matlab: Explicit integral could not be found

2012 12 8
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H=1,R=1,theta=20;
syms x;
syms alpha;
%sigma=F/(2*pi*R*(alpha-1));
z_desh=((x/alpha*x^2+1-alpha)^2-1)^-.5
beta=(sin(theta)+(sin(theta)*sin(theta)+4*alpha*(alpha-1)))/2*alpha
eq=int(z_desh,x,4,1)
when i run the above code en error show like: Warning: Explicit integral could not be found. How to solve this.?
Thanks

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Walter Roberson
Walter Roberson 2012-12-8

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First thing to do is heck whether the x/alpha*x^2 is really what you meant. If it was, why not say x^3/alpha ?
Next, check whether you really want to integrate from 4 down to 1, instead of from 1 to 4.
Thirdly, check why you define beta but then do not use it in what is being integrated.
If your integral is exactly as shown, then there is no readily available analytic form for it. A small number of values of alpha lead to analytic forms; the others do not.

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satendra kumar
satendra kumar 2012-12-8
Please check this, i am still getting the same error...
H=1,R=1,theta=20;
syms x;
syms alpha;
z_desh=1/(x^2/(alpha*x^2 - alpha + 1)^2 - 1)^(1/2)
beta=(sin(theta)+(sin(theta).*sin(theta)+4*alpha*(alpha-1)))/2*alpha
eq=int(z_desh,x,beta,1)
satendra kumar
satendra kumar 2012-12-8
编辑：Walter Roberson 2012-12-8
Hello Roberson,
I guess you can make this out..pls check here is the link of the problem statement
http://prntscr.com/lm4wy
http://prntscr.com/lm52n
Walter Roberson
Walter Roberson 2012-12-8
Question: do you really want sin() of 20 radians? Or do you want sin() of 20 degrees? That would be sind()
Either way, with those beta and z_desh definitions, I get messy analytic solutions involving Elliptic integrals, but whose form depends critically upon the value of alpha in non-obvious ways.
I am getting complex solutions for trial values of alpha. What kind of range were you expecting for alpha ?
satendra kumar
satendra kumar 2012-12-8
编辑：Walter Roberson 2012-12-8
alpha should be a real number with a value less than 1. And consider sind. Pls check this link for the problem statement http://prntscr.com/lm5so
Walter Roberson
Walter Roberson 2012-12-8
Your beta is missing a square root.
beta = (sin(theta) + sqrt(sin(theta)^2 + 4 * alpha * (alpha-1))) / (2*alpha)
My tests so far seem to be indicating that alpha must be at least 1, not less than 1.
satendra kumar
satendra kumar 2012-12-8
That's a relief. Thanks man. May i have your code pls.
Walter Roberson
Walter Roberson 2012-12-8
My code is in Maple, using a facility of Maple that does not translate directly into the MuPAD Symbolic Toolbox
What I determined in the end is that you had better use numeric integration and something like fsolve(), instead of trying to use symbolic integration.
When you do your fsolve(), do not use an alpha less than 1: it is not difficult to demonstrate that alpha between 0 and 1 will generate integrals involving complex values.

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