# [R] Integrate a 1-variable function with 1 parameter (Jose L. Romero)

Moshe Olshansky m_olshansky at yahoo.com
Thu Aug 28 03:57:39 CEST 2008

```This can be done analytically: after changing a variable (2*t -> t) and some scaling we need to compute
f(x) = integral from 0 to 20 of (t^x*exp(-t))dt/factorial(x)

f(0) = int from 0 to 20 of exp(-t)dt = 1 - exp(-20)
and integration by parts yields (for x=1,2,3,...)

f(x) = -exp(-20)*20^x/factorial(x) + f(x-1) so that

f(x) = 1 - exp(-20)*sum(20^k/factorial(k)) where the sum is for k=0,1,...,x

If I did not a mistake, your original quantity should be f(x)/20.

--- On Thu, 28/8/08, jose romero <jlaurentum at yahoo.com> wrote:

> From: jose romero <jlaurentum at yahoo.com>
> Subject: [R] Integrate a 1-variable function with 1 parameter (Jose L. Romero)
> To: r-help at r-project.org
> Received: Thursday, 28 August, 2008, 12:23 AM
> Hey fellas:
>
> I would like to integrate the following function:
>
> integrand <- function (x,t) {
> 	exp(-2*t)*(2*t)^x/(10*factorial(x))
> }
>
> with respect to the t variable, from 0 to 10.
> The variable x here works as a parameter: I would like to
> integrate the said function for each value of x in
> 0,1,..,44.
>
> I have tried Vectorize to no avail.
>
> jose romero
>
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