[R] Graphing the Area of Definite Integral

[William Dunlap]

Your right <- (1:n)*dx mean that your leftmost rectangle's left edge
is at 0, but you want it to be at -4.  You should turn this into a function
so you don't have to remember how the variables in your code depend
on one another.   E.g.,

showIntegral <- function (f, xmin, xmax, n = 16)
{
    curve(f(x), from = xmin, to = xmax, lwd = 2, col = "blue")
    abline(h = 0)
    dx <- (xmax - xmin)/n
    right <- xmin + (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)
}
> showIntegral(f=function(x)x^2, xmin=-4, xmax=4, n=16)
[1] 42.5
> showIntegral(f=function(x)x^2, xmin=-4, xmax=4, n=256)
[1] 42.66602
> showIntegral(f=function(x)x^2, xmin=-4, xmax=4, n=1024)
[1] 42.66663

> 2*4^3/3
[1] 42.66667
> showIntegral
Bill Dunlap
TIBCO Software
wdunlap tibco.com


On Fri, Nov 27, 2015 at 9:50 PM, Steven Stoline <sstoline at gmail.com> wrote:
> 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 <sstoline at gmail.com> wrote:
>
>> many thanks
>>
>> steve
>>
>> On Fri, Nov 27, 2015 at 9:20 AM, peter dalgaard <pdalgd at 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 <sstoline at 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
>>> > sstoline at gmail.com
>>> >
>>> >       [[alternative HTML version deleted]]
>>> >
>>> > ______________________________________________
>>> > R-help at 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.mes at cbs.dk  Priv: PDalgd at gmail.com
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>
>>
>> --
>> Steven M. Stoline
>> 1123 Forest Avenue
>> Portland, ME 04112
>> sstoline at gmail.com
>>
>
>
>
> --
> Steven M. Stoline
> 1123 Forest Avenue
> Portland, ME 04112
> sstoline at gmail.com
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at 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.