Thread Subject:

Numeric integration

Hello,

I want to know how can I calculate the value of this integral

int(int(exp((-y^2)/2)*exp((-x)/2),sqrt(2*x),inf),0,inf)

In this integral the limits if one of the inegral is a variable sqrt(2*x).


Thanks in advance for your help.

"C?sar Ghali" <ceso222@hotmail.com> wrote in message
news:gileq7$jf4$1@fred.mathworks.com...
> Hello,
>
> I want to know how can I calculate the value of this integral
>
> int(int(exp((-y^2)/2)*exp((-x)/2),sqrt(2*x),inf),0,inf)
>
> In this integral the limits if one of the inegral is a variable sqrt(2*x).
>
>
> Thanks in advance for your help.

I did not look at all at what you wrote there in the equation, just
cut/paste, and this is what Matlab returns. may be you can look to see if it
makes sense

EDU>> syms x y
EDU>> int(int(exp((-y^2)/2)*exp((-x)/2),sqrt(2*x),inf),0,inf)

ans =

8/exp(y^2/2)


--Nasser

"C?sar Ghali" <ceso222@hotmail.com> wrote in message <gileq7$jf4$1@fred.mathworks.com>...
> I want to know how can I calculate the value of this integral
> int(int(exp((-y^2)/2)*exp((-x)/2),sqrt(2*x),inf),0,inf)
> In this integral the limits if one of the inegral is a variable sqrt(2*x).

  I assume the inner integration is to be taken with respect to y and the outer integration with respect to x. My symbolic toolbox can't solve it as it stands but if the order of integration is reversing, it can. No numerical quadrature is required; the result is exact.

int(int('exp(-(y^2+x)/2)','y','sqrt(2*x)',inf),'x',0,inf) =
int(int('exp(-(y^2+x)/2)','x',0,'y^2/2'),'y',0,inf) =
(3(sqrt(2)-2*sqrt(3))/3*sqrt(pi)

Roger Stafford