integratelogistic <- function (x, models, beta, lower=0, width, point){
# computes integral (numerically) over x from 0 to width of a
# logistic detection function
integrate(logisticbyx, lower=lower, upper=width,
subdivisions=10, rel.tol=0.01, abs.tol=0.01,
x=x, models=models, beta=beta, point=point)$value
}
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