[R] using integrate with optimize nested in the integration

From: Gregory Gentlemen <gregory_gentlemen_at_yahoo.ca>
Date: Fri 29 Jul 2005 - 05:58:18 EST

Hi guys
im having a problem getting R to numerically integrate for some function, say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this over some finite range, so that here as we integrate over bhat optimize would return a different optimum.  

For instance consider this simple example for which I cannot get R to return the desired result:  

f <- function(bhat) exp(bhat)
g <- function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat integrate(g,lower=0,upper=5)
which returns:
187.499393759 with absolute error < 2.1e-12

However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I intended on getting. Its not identifying that f is a function of bhat ... any advice or ways I can get integrate to not treat this as a constant?

Any help is appreciated.  

Gregoy Gentlemen

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