Integrating a piecewise function with Maxima

Agnishom · 2014-02-22 14:32:39

I wanted to integrate this function

I've tried the following but as you can see, it does not work.

(%i1) f(x) := if x>0 then sin(x) else 0$

(%i2) integrate(f(x),x,-%pi,%pi);
                     %pi
                    /
                    [
(%o2)               I      (if x > 0 then sin(x) else 0) dx
                    ]
                    /
                     - %pi

What to do?

Agnishom · 2014-02-22 15:00:36

Hi Agnishom;

I have no idea how to do this, but you could do the following:

romberg(if x>0 then sin(x) else 0, x, -%pi, %pi);

or perhaps

quad_qags(if x>0 then sin(x) else 0, x, -%pi, %pi);

They integrate the function numerically rather than analytically.

Or better yet, try Mathematica

bobbym · 2014-02-22 15:17:11

Why not just integrate sin(x) between 0 and π?

In geogebra it is done like this.

f(x)=If[x<0,0,1]
g(x)=If[x>=0,1,0]
Integral[f,1,2]
Integral[g,1,2]

Agnishom · 2014-02-22 16:05:04

I tried that but still there are too many 'too many context' errors, also the integration does not work fine.

So, you are an expert geogebra user now.

gAr · 2014-02-22 16:25:05

Example in Sage:

f1(x) = 1
f2(x) = 1-x
f3(x) = x^2-5
f = Piecewise([[(-oo,0),0],[(0,1),f1],[(1,2),f2],[(2,3),f3],[(3,oo),0]])
integrate(f,x,-oo,oo)

= 11/6

Agnishom · 2014-02-22 16:32:29

Sage is very powerful. But it is too huge a download.

What does oo mean?

bobbym · 2014-02-22 20:56:38

Infinity probably.

I can handle geogebra. You will have to find a way to have M around all the time.

Agnishom · 2014-02-22 21:10:48

You will have to find a way to have M around all the time.

Why?

bobbym · 2014-02-22 21:12:03

Hmmm, how can you follow what I am posting if we speak different languages?

gAr · 2014-02-22 21:51:37

Sage is very powerful. But it is too huge a download.

That's true, around 4 GB after decompressing, takes more space than some linux distro installations!
Anyway, you may be having a friend with unlimited data usage plan to download it for you.

What does oo mean?

it's infinity. You may use the full form also

integrate(f,x,-infinity,infinity)

anonimnystefy · 2014-02-22 22:29:15

bobbym wrote:

Hmmm, how can you follow what I am posting if we speak different languages?

We already found that that can be quite a problem.

gAr · 2014-02-22 23:42:06

You will have to find a way to have M around all the time.

Install a native linux in a phone (Ubuntu touch is on its way), and use ARM version of the software! Then can be used with a remote login.

Agnishom · 2014-02-23 03:45:03

gAr wrote:

You will have to find a way to have M around all the time.
Install a native linux in a phone (Ubuntu touch is on its way), and use ARM version of the software! Then can be used with a remote login.

I do not have a smartphone

ARM version of which software? There is a android version of Maxima. Also, why Ubuntu Touch? Ain't Android a linux already?

bobbym · 2014-02-23 06:04:56

Hi Agnishom;

What you could try is using your Windows machine with your CAS when you are on MIF. If you are worried about security then do not go anywhere else while on Windows. When you are finished here then you can reboot and start Linux.

gAr · 2014-02-23 06:13:02

I do not have a smartphone

Me neither! Just telling.

ARM version of which software?

Anything that you wanted to use. Did you know that you can get free Mathematica with Raspberry Pi?

Also, why Ubuntu Touch? Ain't Android a linux already?

Android is linux with Java bloat, owned by morons in or*cle! And to use its applications, you need to trade your identity with g**gle. Now they have billions of identities to give to the governments.

You can use ubuntu touch just like the desktop version. You can even have the terminal applications running, and all the repository is available to the phone also. Though I'm not sure whether they have all the packages for ARM architecture also.

Agnishom · 2014-02-23 13:16:17

Hi bobbym;

Do not worry. I'll be able to run any M command you give within 12 hours whenever needed. And since the forum is not an instant chat cafe, this delay is okay.

bobbym · 2014-02-23 15:49:18

That is very long when we are working on something together. But if that is all you have then it will have to be enough.

Agnishom · 2014-02-23 17:07:43

OK, I will be near my M when we are working on something.

bobbym · 2014-02-23 17:52:06

Do you know that a Fourier series can also help sum another series?

Agnishom · 2014-02-23 21:24:07

No, and I do not see how a Fourier series is useful.

bobbym · 2014-02-23 22:19:04

The graphs should be showing you that they are useful to approximate other functions.

Agnishom · 2014-02-27 02:01:26

I beg your pardon?

bobbym · 2014-02-27 02:02:56

Agnishom wrote:

No, and I do not see how a Fourier series is useful.

bobbym wrote:

The graphs should be showing you that they are useful to approximate other functions.

Agnishom · 2014-02-27 02:11:47

Why should that be useful?

May I ask you a different question about M usage?

bobbym · 2014-02-27 02:16:37

Because after polynomials, trig terms are the next easiest to compute. So it just natural that we would want to approximate difficult functions with bunches of easier ones.

May I ask you a different question about M usage?

Hmm, what question? And maybe you should make a new thread for it.

Math Is Fun Forum

#1 2014-02-22 14:32:39

Integrating a piecewise function with Maxima

#2 2014-02-22 15:00:36

Re: Integrating a piecewise function with Maxima

#3 2014-02-22 15:17:11

Re: Integrating a piecewise function with Maxima

#4 2014-02-22 16:05:04

Re: Integrating a piecewise function with Maxima

#5 2014-02-22 16:25:05

Re: Integrating a piecewise function with Maxima

#6 2014-02-22 16:32:29

Re: Integrating a piecewise function with Maxima

#7 2014-02-22 20:56:38

Re: Integrating a piecewise function with Maxima

#8 2014-02-22 21:10:48

Re: Integrating a piecewise function with Maxima

#9 2014-02-22 21:12:03

Re: Integrating a piecewise function with Maxima

#10 2014-02-22 21:51:37

Re: Integrating a piecewise function with Maxima

#11 2014-02-22 22:29:15

Re: Integrating a piecewise function with Maxima

#12 2014-02-22 23:42:06

Re: Integrating a piecewise function with Maxima

#13 2014-02-23 03:45:03

Re: Integrating a piecewise function with Maxima

#14 2014-02-23 06:04:56

Re: Integrating a piecewise function with Maxima

#15 2014-02-23 06:13:02

Re: Integrating a piecewise function with Maxima

#16 2014-02-23 13:16:17

Re: Integrating a piecewise function with Maxima

#17 2014-02-23 15:49:18

Re: Integrating a piecewise function with Maxima

#18 2014-02-23 17:07:43

Re: Integrating a piecewise function with Maxima

#19 2014-02-23 17:52:06

Re: Integrating a piecewise function with Maxima

#20 2014-02-23 21:24:07

Re: Integrating a piecewise function with Maxima

#21 2014-02-23 22:19:04

Re: Integrating a piecewise function with Maxima

#22 2014-02-27 02:01:26

Re: Integrating a piecewise function with Maxima

#23 2014-02-27 02:02:56

Re: Integrating a piecewise function with Maxima

#24 2014-02-27 02:11:47

Re: Integrating a piecewise function with Maxima

#25 2014-02-27 02:16:37

Re: Integrating a piecewise function with Maxima

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