Is it possible to calculate an integral in GAMS?

[anaaza]

Hi,

I need to calculate the volume of a tree by integrating the "taper" function below. I did this code in R, and it works well, but now that I am trying to code it in GAMS I cannot find a way of doing that.
How do we calculate integrals in GAMS?
Any suggestions?

---------------

midh <- 13.5
midd <- 15.1

taper1 <- function(midh){
taper2 <- function(midd){
tFactorSBD <- 1.3/midh
qFactorSBD <- (0/100)/midh
YFactorSBD <- (1-qFactorSBD^0.5)/(1-tFactorSBD^0.5)
aux1SBD <- 0.6624965*(YFactorSBD^0.1)+ 0.3781478*(qFactorSBD^4)
aux2SBD <- -0.4418430*asin(1-sqrt(qFactorSBD))
aux3SBD <- -0.5154988/exp(midd/midh)
aux4SBD <- 0.0197963*midd^YFactorSBD
ExpFactorSBD <- aux1SBD+ aux2SBD+ aux3SBD+ aux4SBD
diam <- 0.8795844*(midd^0.9457765)*(midh^0.1061692)*(YFactorSBD^ExpFactorSBD)
area<- pi*((diam/2)^2)/10000
}
}

volume<- function(midh){
integrate(taper1(midh), lower = 0,upper = midh)$value
}
------------------
Thanks

Ana

[Manassaldi]

hi, i think you should use an analytic integration (if possible) otherwise make a numerical integration (like simpson rule).

[SapperDoc]

Whereas Simpson's Rule or even the Trapezoid Rule are theoretically preferable to the Left Hand Rule or Right Hand Rule, one can just integrate with a higher granularity (i.e., smaller intervals) and use one of the simpler approaches. A "loop" structure works nicely, incrementally adding the area under the next segment of the function to a scalar.