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From: vlajchek on 16 Jun 2010 13:39
hello,

I have a problem with the use of quad function in Matlab for numerical integration. Let me try to explain on an example. When I want to find the integral of expression exp(-x^2/2) from 0 to infinity, where for the higher limit I use some very large number:

Q = quad('exp(-x.^2./2)',0,10000000000)

I get the correct result sqrt(pi/2)=1.2533.
If I try to use the same logic for the expression x*exp(-x^2/2) for the same limits:

Q = quad('x.*exp(-x.^2./2)',0,10000000000)

I get the result 0, although I know that correct result for this integral is 1.

What can potentialy be the problem? The thing is I am solving some more difficult integrals, without analytical solutions, but in some way similar to this example, and I always get 0 where I don't expect it using the quad function.

Thank you in advance...
From: Steven Lord on 16 Jun 2010 17:59

"vlajchek" <v_despotovic(a)yahoo.com> wrote in message
news:2106186614.357396.1276724379296.JavaMail.root(a)gallium.mathforum.org...
> hello,
>
> I have a problem with the use of quad function in Matlab for numerical
> integration. Let me try to explain on an example. When I want to find the
> integral of expression exp(-x^2/2) from 0 to infinity, where for the
> higher limit I use some very large number:
>
> Q = quad('exp(-x.^2./2)',0,10000000000)
>
> I get the correct result sqrt(pi/2)=1.2533.
> If I try to use the same logic for the expression x*exp(-x^2/2) for the
> same limits:
>
> Q = quad('x.*exp(-x.^2./2)',0,10000000000)
>
> I get the result 0, although I know that correct result for this integral
> is 1.
>
> What can potentialy be the problem? The thing is I am solving some more
> difficult integrals, without analytical solutions, but in some way similar
> to this example, and I always get 0 where I don't expect it using the quad
> function.

http://www.mathworks.com/matlabcentral/newsreader/view_thread/122969#310160

http://www.mathworks.com/matlabcentral/newsreader/view_thread/246456

Choose a _smaller_ interval (but one that still covers the whole region
where your function is "interesting") over which to integrate the function.
When I evaluate your integrand at x = 30, the answer is on the order of
1e-194 so that's probably good enough; if you want the integrand to be
exactly 0 in double precision, use 50 as your upper limit instead. There's
no need to use as large an upper limit as you did.

quad(@(x) x.*exp(-x.^2/2), 0, 50)

--
Steve Lord
slord(a)mathworks.com
comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
To contact Technical Support use the Contact Us link on
http://www.mathworks.com


From: vlajchek on 17 Jun 2010 08:41
Thanks Steve,

it is still not easy to find a good interval of integration for the integrals I have to solve, but it's a good starting point
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