Integration with both limits variable

Hi, I am trying to solve an integration where both limits are variable. The function itself being integrated is simple, it is just exp(-W^2). I can solve the inegration fine using this method without limits - the limits are the issue here. I think it could be because of the use of the symbolic functions to integrate? But I have tried other methods, and I cannot get it to work with these limits. I get the error:

error in sym/subsref (line 898)

R_tilde = builtin('subsref',L_tilde,Idx);

The upper limit is -phi, and the lower limit is beta-phi.

Another issue could be because the upper limit is the same as the variable being integrated. However I don't know how to get around that issue either?

I have just shown some of my code, hopefully this is enough to make sense of what I am trying to do. Any help would be greatly appreciated!

t=linspace(0,1000);
r=linspace(0,100);
D=2;
beta=r./sqrt(4*D.*t);
phi=U.*sqrt(t./D);
W=beta-phi;

% Performing integration
syms W 
f=exp(-(W.^2));
a=-phi;
b=beta-phi;
int(f,W,a,b)

[Bjorn Gustavsson]

Use the error-function, erf, and then you're done - if this is your full problem...

[Sophie Malcolm]

Hi Bjorn,

Thank you so much for your response, I hadn't considered the use of the error function in MATLAB and will look into that now!

Thanks so much,

Sophie

[Bjorn Gustavsson]

Your solution is simply:

(pi^(1/2)*(erf(b) - erf(a)))/2.

Answer 1

[Ameer Hamza]

You are getting an error because you are passing arrays (a and b) to int() as its limit. The limits must be scalar. For example, try this

t=linspace(0,1000);
r=linspace(0,100);
D=2;
U = 3;
beta=r./sqrt(4*D.*t);
phi=U.*sqrt(t./D);
W=beta-phi;

% Performing integration
syms W 
f=exp(-(W.^2));
a=-phi;
b=beta-phi;
int(f,W,a(2),b(2))

[Sophie Malcolm]

Hi Ameer,

Thank you so much for this, I didn't realise that! That is so helpful, thanks a lot.

Sophie

[Ameer Hamza]

I am glad to be of help!

Answer 2

[Bjorn Gustavsson]

Matlab has both a numerical and a symbolic version of the error-function. That will be the answer to your problem. The numeric version is vectorized, so it can handle your inputs without problems.

HTH

[Sophie Malcolm]

Hi,

Okay that makes a lot of sense! Thank you so much for explaining. I will look into that now.

Thanks for your help,

Sophie