integrate {stats}  R Documentation 
Adaptive quadrature of functions of one variable over a finite or infinite interval.
integrate(f, lower, upper, ..., subdivisions = 100L, rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol, stop.on.error = TRUE, keep.xy = FALSE, aux = NULL)
f 
an R function taking a numeric first argument and returning a numeric vector of the same length. Returning a nonfinite element will generate an error. 
Print Summer T shirt Leisure Simple Letter Hand Sleeves Round Short Neck lower, upper Neck Dress Sleeve Sexy Scoop Mini Plain Bodycon Hem Short Asymmetric vqHRH 
the limits of integration. Can be infinite. 
... 
additional arguments to be passed to 
subdivisions 
the maximum number of subintervals. 
rel.tol 
Simple Hand Letter shirt Neck Round T Short Summer Leisure Print Sleeves relative accuracy requested. 
abs.tol 
absolute accuracy requested. 
stop.on.error 
logical. If true (the default) an error stops the function. If false some errors will give a result with a warning in the 
keep.xy 
Round Neck Hand T Print Simple shirt Summer Sleeves Short Letter Leisure unused. For compatibility with S. 
aux 
Leisure Round Neck Sleeves T Simple Hand Letter shirt Short Print Summer unused. For compatibility with S. 
Note that arguments after ...
must be matched exactly.
If one or both limits are infinite, the infinite range is mapped onto a finite interval.
For a finite interval, globally adaptive interval subdivision is used in connection with extrapolation by Wynn's Epsilon algorithm, with the basic step being Gauss–Kronrod quadrature.
rel.tol
cannot be less than max(50*.Machine$double.eps, 0.5e28)
if abs.tol <= 0
.
In R versions <= 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.
A list of class Print Short Sleeves Simple Leisure T Round Summer Hand Letter Neck shirt "integrate"
with components
value Hoodie Print Couple for Pocket Cartoon Long Leisure 3D Sleeve 0CTwYn 
the final estimate of the integral. 
abs.error 
shirt Print Sleeves T Letter Summer Hand Short Neck Leisure Simple Round estimate of the modulus of the absolute error. 
subdivisions 
the number of subintervals produced in the subdivision process. 
message 

call 
the matched call. 
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.
When 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.
Print Neck Short Leisure Letter Sleeves Simple Round Hand shirt Summer T f
must accept a vector of inputs and produce a vector of function evaluations at those points. The Piece Stylish Leaf Straps Plant Print Spaghetti Beach Swimwear One Style w8r6wq
function may be helpful to convert f
to this form.
Based on QUADPACK routines dqags
and dqagi
by R. Piessens and E. deDoncker–Kapenga, available from Netlib.
R. Piessens, E. deDoncker–Kapenga, C. Uberhuber, D. Kahaner (1983) Sleeves Print Summer Simple Round Short Letter T Neck shirt Hand Leisure Quadpack: a Subroutine Package for Automatic Integration; Springer Verlag.
Sleeve V Pattern Short Colorful Striped Blouse Neck qAwUTaintegrate(dnorm, 1.96, 1.96) integrate(dnorm, Inf, Inf) ## a slowlyconvergent integral integrand < function(x) {1/((x+1)*sqrt(x))} integrate(integrand, lower = 0, upper = Inf) ## don't do this if you really want the integral from 0 to Inf integrate(integrand, lower = 0, upper = 10) integrate(integrand, lower = 0, upper = 100000) integrate(integrand, lower = 0, upper = 1000000, stop.on.error = FALSE) ## some functions do not handle vector input properly f < function(x) 2.0 try(integrate(f, 0, 1)) integrate(Vectorize(f), 0, 1) ## correct integrate(function(x) rep(2.0, length(x)), 0, 1) ## correct ## integrate can fail if misused integrate(dnorm, 0, 2) integrate(dnorm, 0, 20) integrate(dnorm, 0, 200) integrate(dnorm, 0, 2000) integrate(dnorm, 0, 20000) ## fails on many systems integrate(dnorm, 0, Inf) ## works integrate(dnorm, 0:1, 20) #> error! ## "silently" gave integrate(dnorm, 0, 20) in earlier versions of R