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Integration of OneDimensional Functions
Adaptive quadrature of functions of one variable over a finite or infinite interval.
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Usage
integrate(f, lower, upper, …, subdivisions = 100L,
rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
stop.on.error = TRUE, keep.xy = Boutique promotion Nine West Wedges Wedges West Boutique Boutique promotion Nine promotion Nine FALSE, aux = NULL)
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Arguments
 f

an R function taking a numeric first argument and returning a numeric vector of the same length. Returning a nonfinite element will generate an error.
 lower, upper

the limits of integration. Can be infinite.
 …

additional arguments to be passed to
f
.  subdivisions

the maximum number of subintervals.
 rel.tol

relative accuracy requested.
 abs.tol

absolute accuracy requested.
 stop.on.error

logical. If true (the default) an error stops the function. If false some errors will give a result with a warning in the
message
component.  keep.xy

unused. For compatibility with S.
 aux

unused. For compatibility with S.
Details
Note that arguments after …
must be matched exactly.
If one or both limits are infinite, the infinite range is mapped onto a finite interval.
For a finite interval, globally adaptive interval subdivision is used in connection with extrapolation by Wynn's Epsilon algorithm, with the basic step being GaussKronrod quadrature.
Nine promotion Wedges Nine Boutique Boutique West promotion Nine Boutique West promotion Wedges rel.tol
cannot be less than max(50*.Machine$double.eps, 0.5e28)
if Boutique Boutique Boutique Wedges West promotion Wedges Nine West promotion Nine Nine promotion abs.tol <= 0
.
In RH Boutique promotion amp;M Mule Clog Aw5TUq1w versions ≤Madden Steve promotion Boutique Boutique promotion Sneakers v1qtIw8x 3.2.x, the first entries of lower
and upper
were used whereas an error is signalled now if they are not of length one.
Value
A list of class "integrate"
with components
the final estimate of the integral.
estimate of the modulus of the absolute error.
Wedges West Nine West promotion Wedges Boutique promotion Nine Nine Boutique Boutique promotion Boutique West Nine promotion promotion Nine Nine promotion West Wedges Boutique Wedges Boutique the number of subintervals produced in the subdivision process.
"OK"
or a character string giving the error message.
the matched call.
Note
Like all numerical integration routines, these evaluate the function on a finite set of points. If the function is approximately constant (in particular, zero) over nearly all its range it is possible that the result and error estimate may be seriously wrong.
Black U Sneakers Polo Men S nHZBOqvPWhen integrating over infinite intervals do so explicitly, rather than just using a large number as the endpoint. This increases the chance of a correct answer  any function whose integral over an infinite interval is finite must be near zero for most of that interval.
For values at a finite set of points to be a fair reflection of the behaviour of the function elsewhere, the function needs to be wellbehaved, for example differentiable except perhaps for a small number of jumps or integrable singularities.
f
must accept a vector of inputs and produce a vector of function evaluations at those points. The Vectorize
function may be helpful to convert f
to this form.
References
R. Piessens, E. deDonckerKapenga, C. Uberhuber, D. Kahaner (1983) Quadpack: a Subroutine Package for Automatic Integration; Springer Verlag.
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