[R] Graphing the Area of Definite Integral

[Steven Stoline]

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]]