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Thread Subject:
Warning: Explicit integral could not be found.

Subject: Warning: Explicit integral could not be found.

From: Ferra

Date: 26 Jun, 2013 01:26:22

Message: 1 of 5

Hi

I'm trying to solve this integration but it gives me this error:
Warning: Explicit integral could not be found.

 syms a b
 Q = (1/(2*pi*lams)) * exp( - (a^2 + b^2)/(2*lams));
 q = int(int(Q,b,0,sqrt((lams^2) - (a^2))),a,0,lams);

Subject: Warning: Explicit integral could not be found.

From: Torsten

Date: 26 Jun, 2013 06:34:16

Message: 2 of 5

"Ferra " <ferra.xu@yahoo.com> wrote in message <kqdfvu$psn$1@newscl01ah.mathworks.com>...
> Hi
>
> I'm trying to solve this integration but it gives me this error:
> Warning: Explicit integral could not be found.
>
> syms a b
> Q = (1/(2*pi*lams)) * exp( - (a^2 + b^2)/(2*lams));
> q = int(int(Q,b,0,sqrt((lams^2) - (a^2))),a,0,lams);

Use numerical integration for the function received by the inner integral.

Best wishes
Torsten.

Subject: Warning: Explicit integral could not be found.

From: Torsten

Date: 26 Jun, 2013 06:56:07

Message: 3 of 5

"Torsten" wrote in message <kqe218$49a$1@newscl01ah.mathworks.com>...
> "Ferra " <ferra.xu@yahoo.com> wrote in message <kqdfvu$psn$1@newscl01ah.mathworks.com>...
> > Hi
> >
> > I'm trying to solve this integration but it gives me this error:
> > Warning: Explicit integral could not be found.
> >
> > syms a b
> > Q = (1/(2*pi*lams)) * exp( - (a^2 + b^2)/(2*lams));
> > q = int(int(Q,b,0,sqrt((lams^2) - (a^2))),a,0,lams);
>
> Use numerical integration for the function received by the inner integral.
>
> Best wishes
> Torsten.

Or much better:
Perform integration in polar coordinates.

Best wishes
Torsten.

Subject: Warning: Explicit integral could not be found.

From: Christopher Creutzig

Date: 22 Jul, 2013 09:21:08

Message: 4 of 5

On 26.06.13 03:26, Ferra wrote:

> I'm trying to solve this integration but it gives me this error:
> Warning: Explicit integral could not be found.
>
> syms a b
> Q = (1/(2*pi*lams)) * exp( - (a^2 + b^2)/(2*lams));
> q = int(int(Q,b,0,sqrt((lams^2) - (a^2))),a,0,lams);

I'm not sure what lams is, but even assuming it is an unspecified
symbolic variable, changing the order of integration yields a
closed-form integral:

>> syms lams
>> q = int(int(Q,a,0,lams),b,0,sqrt((lams^2) - (a^2)))

q =

(5734161139222659*pi*erf((2^(1/2)*lams)/2)*erf((2^(1/2)*(lams^2 -
a^2)^(1/2))/2))/72057594037927936


SMT neither has some explicit notion of “double integral,” nor does it
check whether your integrand fulfills the conditions of Fubini's theorem
to allow exchanging the order of integration (which happens to be the
case here, at least if a, b, and lams are finite and real, and lams is
positive). That is something you need to do yourself.



HTH,

Christopher

Subject: Warning: Explicit integral could not be found.

From: Torsten

Date: 22 Jul, 2013 13:38:12

Message: 5 of 5

Christopher Creutzig <Christopher.Creutzig@mathworks.com> wrote in message <51ECF984.7080907@mathworks.com>...
> On 26.06.13 03:26, Ferra wrote:
>
> > I'm trying to solve this integration but it gives me this error:
> > Warning: Explicit integral could not be found.
> >
> > syms a b
> > Q = (1/(2*pi*lams)) * exp( - (a^2 + b^2)/(2*lams));
> > q = int(int(Q,b,0,sqrt((lams^2) - (a^2))),a,0,lams);
>
> I'm not sure what lams is, but even assuming it is an unspecified
> symbolic variable, changing the order of integration yields a
> closed-form integral:
>
> >> syms lams
> >> q = int(int(Q,a,0,lams),b,0,sqrt((lams^2) - (a^2)))
>
> q =
>
> (5734161139222659*pi*erf((2^(1/2)*lams)/2)*erf((2^(1/2)*(lams^2 -
> a^2)^(1/2))/2))/72057594037927936
>
>
> SMT neither has some explicit notion of “double integral,” nor does it
> check whether your integrand fulfills the conditions of Fubini's theorem
> to allow exchanging the order of integration (which happens to be the
> case here, at least if a, b, and lams are finite and real, and lams is
> positive). That is something you need to do yourself.
>
>
>
> HTH,
>
> Christopher

a is the second variable of integration - so it should not be part of the solution.
The solution for the integral
  q = int(int(Q,b,0,sqrt((lams^2) - (a^2))),a,0,lams);
should come out as
 q = 0.25*(1-exp(-lams/2))

Best wishes
Torsten.

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