Re: Piecewise and Integral

• To: mathgroup at smc.vnet.net
• Subject: [mg75239] Re: Piecewise and Integral
• From: dh <dh at metrohm.ch>
• Date: Sat, 21 Apr 2007 23:13:52 -0400 (EDT)
• References: <f09g01\$pe\$1@smc.vnet.net>

```
\$Version: 5.1 for Microsoft Windows (October 25, 2004)

Hi,

I am getting 10 as expected. Are you fooling yourself?

Daniel

zosi wrote:

> Hi,

>

> I have a problem that I considered (and still consider) trivial.

>

> Let us suppose I have defined a Gate

> (Period T and width \[Tau]= T/4), through Piecewise

> and extended it periodically (see from In[1] to In[6]).

> The Plot seems indicate that the extension is correct.

> Now let us calculate the coefficient a0 according to

> the usual formula In[13], having assumed that  \[Lambda]=0  (In[12])

> The result Out[13] = 10  is correct.

>

> If I consider another case, i.e., I change the value of \[Lambda]=1/10,

> the result, 10,  is again correct  (as expected !).

>

> But, if I try \[Lambda]= T/2 the result is 5 (instead of 10). Why ?

> My interpretation is that the range

> \[Tau]< x \[LessEqual]  T/2 is not evaluated.

> Infact, when I remove  the ":"  in  In[3], the function is not defined

> in the last interval ( but correctly Plotted !).

>

> Any hint  to obtain  10 when \[Lambda]= T/2 ?

>

> G. Zosi

> Dipartimento Fisica Generale

> Universita di Torino

> Italy

>

>  ----------------- begin -----------------------

>

> In[1]:= Clear["Global`*"] ; Remove["Global`*"];\$Line=0;

>

> In[1]:= T=2;

>

> In[2]:= \[Tau]= T/4.

>

> In[3]:=   f[x_] := Piecewise[ {{0,  -T/2 \[LessEqual] x <- \[Tau]},

>                               {10, -\[Tau] \[LessEqual]   x

> \[LessEqual]\[Tau]},

>                                {0,     \[Tau]< x \[LessEqual]  T/2}}]

>

> In[4]:= f[x_]:=f[x-T]/;x >T/2

>

> In[5]:= f[x_]:=f[x+T]/;x<-T/2

>

> In[6]:= Plot[f[x],{x,-2 T,2 T}];

>

> In[12]:= \[Lambda]=0

>

> In[13]:= a0 = (2/T)*Integrate[f[x],{x,-T/2. +\[Lambda] ,T/2.+\[Lambda]}]

>

> Out[13] = 10

>

>    Now try with  \[Lambda] = 1/10   and \[Lambda] = T/2

>

>    --------------------- end --------------------

>

```

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