Dear Peter: in my previous email I forgot to reply to the list too I used your code for more than one examples, and it works nicely. But when I tried to use for the the function: f(x) = x^2, it looks like I am missing something, but I could not figured it out.
This what I used: f <- function(x) x^2 curve(f(x), from=-4, to=4, lwd=2, col="blue") abline(h=0) n <- 16 dx <- 8/n right <- (1:n)*dx left <- right - dx mid <- right - dx/2 fm <- f(mid) rect(left,0,right,fm, density = 20, border = "red") points(mid, fm, col = "red", cex = 1.25, pch=19) sum(fm*dx) 1/3 * (64+64) with many thanks steve On Fri, Nov 27, 2015 at 3:36 PM, Steven Stoline <sstol...@gmail.com> wrote: > many thanks > > steve > > On Fri, Nov 27, 2015 at 9:20 AM, peter dalgaard <pda...@gmail.com> wrote: > >> Something like this? >> >> f <- function(x) x^3-2*x >> curve(f(x), from=0, to=4) >> abline(h=0) >> n <- 16 >> dx <- 4/n >> right <- (1:n)*dx >> left <- right - dx >> mid <- right - dx/2 >> fm <- f(mid) >> points(mid, fm) >> rect(left,0,right,fm) >> >> sum(fm*dx) >> >> 1/4 * 4^4 - 4^2 >> >> >> -pd >> >> >> On 27 Nov 2015, at 13:52 , Steven Stoline <sstol...@gmail.com> wrote: >> >> > Dear All: >> > >> > I am trying to explain to my students how to calculate the definite >> > integral using the Riemann sum. Can someone help me to graph the area >> under >> > the curve of the function, showing the curve as well as the rectangles >> > between 0 and 4.. >> > >> > *f(x) = x^3 - 2*x * >> > >> > over the interval [0 , 4] >> > >> > >> > >> > with many thanks >> > steve >> > >> > -- >> > Steven M. Stoline >> > 1123 Forest Avenue >> > Portland, ME 04112 >> > sstol...@gmail.com >> > >> > [[alternative HTML version deleted]] >> > >> > ______________________________________________ >> > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >> > https://stat.ethz.ch/mailman/listinfo/r-help >> > PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> > and provide commented, minimal, self-contained, reproducible code. >> >> -- >> Peter Dalgaard, Professor, >> Center for Statistics, Copenhagen Business School >> Solbjerg Plads 3, 2000 Frederiksberg, Denmark >> Phone: (+45)38153501 >> Office: A 4.23 >> Email: pd....@cbs.dk Priv: pda...@gmail.com >> >> >> >> >> >> >> >> >> >> > > > -- > Steven M. Stoline > 1123 Forest Avenue > Portland, ME 04112 > sstol...@gmail.com > -- Steven M. Stoline 1123 Forest Avenue Portland, ME 04112 sstol...@gmail.com [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
