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Re: [obm-l] Integral[Sen(x)/(1+x)](Desafio)



   Caro Leandro,
   Eu nao lembro de ter feito essa conta, mas posso fazer. Por outro lado,
nao e' Tammus, e' Tamm... :-)
   Derivando Si(x+1)Cos(1) - Ci(x+1)Sen(1) obtemos
Cos(1).Sen(x+1)/(x+1)-Sen(1)(1/(x+1)+((Cos(x+1)-1)/(x+1))=
=(Cos(1).Sen(x+1)-Sen(1).Cox(x+1))/(x+1)=Sen((x+1)-1)/(x+1)=Sen(x)/(x+1).
   Abracos,
            Gugu

>   
>
>O que eu acho que ele quer Claudio e chegar nesse resultado. Porem, se
>nao me engano, o Carlos Tammus (Gugu) ja fez essa resolucao
>anteriormente.=20
>
>=20
>
>Caso ele queira somente verificar, entao esta correto !!!=20
>
>=20
>
>Saudacoes Rubro-Negras,
>
>=20
>
>Leandro.=20
>
>=20
>
>-----Original Message-----
>From: owner-obm-l@sucuri.mat.puc-rio.br
>[mailto:owner-obm-l@sucuri.mat.puc-rio.br] On Behalf Of claudio.buffara
>Sent: Tuesday, June 10, 2003 9:35 AM
>To: obm-l
>Subject: Re:[obm-l] Integral[Sen(x)/(1+x)](Desafio)
>
>=20
>
>=C9 s=F3 derivar o lado direito, levando em conta que:
>
>d(ln(x))/dx =3D 1/x=20
>
>e
>
>d(integral(f(t), t=3D0..x)/dx =3D f(x)
>
>=20
>
>Um abra=E7o,
>
>Claudio.
>
>=20
>
>
>De:
>
>owner-obm-l@sucuri.mat.puc-rio.br
>
>
>Para:
>
>obm-l@mat.puc-rio.br
>
>=20
>
>
>C=F3pia:
>
>augusto_math@yahoo.com.br
>
>
>Data:
>
>Tue, 10 Jun 2003 11:58:02 -0300 (ART)
>
>=20
>
>
>Assunto:
>
>[obm-l] Integral[Sen(x)/(1+x)](Desafio)
>
>
>=20
>
>=20
>
>> Algu=E9m se habilita a demonstrar que
>
>>=20
>
>> int[Sen(x)/(1+x), x] =3D Si(x+1)Cos(1) - Ci(x+1)Sen(1)
>
>>=20
>
>> Si: Seno integral
>
>> Ci: Cosseno integral
>
>>=20
>
>> Estas integrais s=E3o definidas para todo x complexo=20
>
>> como segue
>
>>=20
>
>> Si(t) =3D int[Sen(t)/t, t=3D0..x]
>
>> Ci(t) =3D gamma + ln(x) + int[(Cos(t)-1)/t, t=3D0..x]
>
>>=20
>
>> Obrigado, desde j=E1.
>
>>=20
>
>>=20
>
>>
>_______________________________________________________________________
>
>> Yahoo! GeoCities
>
>> Tudo para criar o seu site: ferramentas f=E1ceis de usar, espa=E7o de
>sobra e acess=F3rios.
>
>> http://br.geocities.yahoo.com/
>
>>
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
>=3D
>
>> Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
>
>> http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html
>
>>
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
>=3D
>
>>=20
>
>>=20
>
>
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><div class=3DSection1>
>
><p class=3DMsoNormal><font size=3D2 color=3Dnavy face=3DArial><span =
>lang=3DPT-BR
>style=3D'font-size:10.0pt;font-family:Arial;color:navy'>O que eu acho =
>que ele
>quer Claudio e chegar nesse resultado. Porem, se nao me engano, o Carlos =
>Tammus
>(Gugu) ja fez essa resolucao anteriormente. </span></font></p>
>
><p class=3DMsoNormal><font size=3D2 color=3Dnavy face=3DArial><span =
>lang=3DPT-BR
>style=3D'font-size:10.0pt;font-family:Arial;color:navy'>&nbsp;</span></fo=
>nt></p>
>
><p class=3DMsoNormal><font size=3D2 color=3Dnavy face=3DArial><span =
>lang=3DPT-BR
>style=3D'font-size:10.0pt;font-family:Arial;color:navy'>Caso ele queira =
>somente
>verificar, entao esta correto !!! </span></font></p>
>
><p class=3DMsoNormal><font size=3D2 color=3Dnavy face=3DArial><span =
>lang=3DPT-BR
>style=3D'font-size:10.0pt;font-family:Arial;color:navy'>&nbsp;</span></fo=
>nt></p>
>
><p class=3DMsoNormal><font size=3D2 color=3Dnavy face=3DArial><span =
>lang=3DPT-BR
>style=3D'font-size:10.0pt;font-family:Arial;color:navy'>Saudacoes =
>Rubro-Negras,</span></font></p>
>
><p class=3DMsoNormal><font size=3D2 color=3Dnavy face=3DArial><span =
>lang=3DPT-BR
>style=3D'font-size:10.0pt;font-family:Arial;color:navy'>&nbsp;</span></fo=
>nt></p>
>
><p class=3DMsoNormal><font size=3D2 color=3Dnavy face=3DArial><span =
>lang=3DPT-BR
>style=3D'font-size:10.0pt;font-family:Arial;color:navy'>Leandro. =
></span></font></p>
>
><p class=3DMsoNormal><font size=3D2 color=3Dnavy face=3DArial><span =
>lang=3DPT-BR
>style=3D'font-size:10.0pt;font-family:Arial;color:navy'>&nbsp;</span></fo=
>nt></p>
>
><p class=3DMsoNormal><font size=3D2 face=3DTahoma><span =
>style=3D'font-size:10.0pt;
>font-family:Tahoma'>-----Original Message-----<br>
><b><span style=3D'font-weight:bold'>From:</span></b> =
>owner-obm-l@sucuri.mat.puc-rio.br
>[mailto:owner-obm-l@sucuri.mat.puc-rio.br] <b><span =
>style=3D'font-weight:bold'>On
>Behalf Of </span></b>claudio.buffara<br>
><b><span style=3D'font-weight:bold'>Sent:</span></b> Tuesday, June 10, =
>2003 9:35
>AM<br>
><b><span style=3D'font-weight:bold'>To:</span></b> obm-l<br>
><b><span style=3D'font-weight:bold'>Subject:</span></b> Re:[obm-l]
>Integral[Sen(x)/(1+x)](Desafio)</span></font></p>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&nbsp;</span></font></p>
>
><div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>=C9 s=F3 derivar o lado direito, levando em conta =
>que:</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>d(ln(x))/dx =3D 1/x </span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>e</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>d(integral(f(t), t=3D0..x)/dx =3D f(x)</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&nbsp;</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>Um abra=E7o,</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>Claudio.</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&nbsp;</span></font></p>
>
></div>
>
><div>
>
><table class=3DMsoNormalTable border=3D0 cellspacing=3D0 cellpadding=3D0 =
>width=3D500
> style=3D'width:250.0pt'>
> <tr>
>  <td width=3D100 bgcolor=3D"#D8D8D8" =
>style=3D'width:50.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><b><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial";
>  font-weight:bold'>De:</span></font></b></p>
>  </td>
>  <td width=3D400 bgcolor=3D"#D8D8D8" =
>style=3D'width:200.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial"'>owner-obm-l@sucuri.mat.puc-rio.br</span></font></p>
>  </td>
> </tr>
></table>
>
></div>
>
><table class=3DMsoNormalTable border=3D0 cellspacing=3D0 cellpadding=3D0 =
>width=3D500
> style=3D'width:250.0pt'>
> <tr>
>  <td width=3D100 bgcolor=3D"#D8D8D8" =
>style=3D'width:50.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><b><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial";
>  font-weight:bold'>Para:</span></font></b></p>
>  </td>
>  <td width=3D400 bgcolor=3D"#D8D8D8" =
>style=3D'width:200.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial"'>obm-l@mat.puc-rio.br</span></font></p>
>  </td>
> </tr>
></table>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt;display:none'>&nbsp;</span></font></p>
>
><table class=3DMsoNormalTable border=3D0 cellspacing=3D0 cellpadding=3D0 =
>width=3D500
> style=3D'width:250.0pt'>
> <tr>
>  <td width=3D100 bgcolor=3D"#D8D8D8" =
>style=3D'width:50.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><b><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial";
>  font-weight:bold'>C=F3pia:</span></font></b></p>
>  </td>
>  <td width=3D400 bgcolor=3D"#D8D8D8" =
>style=3D'width:200.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial"'>augusto_math@yahoo.com.br</span></font></p>
>  </td>
> </tr>
></table>
>
></div>
>
><table class=3DMsoNormalTable border=3D0 cellspacing=3D0 cellpadding=3D0 =
>width=3D500
> style=3D'width:250.0pt'>
> <tr>
>  <td width=3D100 bgcolor=3D"#D8D8D8" =
>style=3D'width:50.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><b><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial";
>  font-weight:bold'>Data:</span></font></b></p>
>  </td>
>  <td width=3D400 bgcolor=3D"#D8D8D8" =
>style=3D'width:200.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial"'>Tue, 10
>  Jun 2003 11:58:02 -0300 (ART)</span></font></p>
>  </td>
> </tr>
></table>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt;display:none'>&nbsp;</span></font></p>
>
><table class=3DMsoNormalTable border=3D0 cellspacing=3D0 cellpadding=3D0 =
>width=3D500
> style=3D'width:250.0pt'>
> <tr>
>  <td width=3D100 bgcolor=3D"#D8D8D8" =
>style=3D'width:50.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><b><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial";
>  font-weight:bold'>Assunto:</span></font></b></p>
>  </td>
>  <td width=3D400 bgcolor=3D"#D8D8D8" =
>style=3D'width:200.0pt;background:#D8D8D8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><font size=3D2 face=3D"Trebuchet MS; verdana; =
>arial"><span
>  style=3D'font-size:10.0pt;font-family:"Trebuchet MS\; verdana\; =
>arial"'>[obm-l]
>  Integral[Sen(x)/(1+x)](Desafio)</span></font></p>
>  </td>
> </tr>
></table>
>
></div>
>
><table class=3DMsoNormalTable border=3D0 cellspacing=3D0 cellpadding=3D0 =
>width=3D500
> style=3D'width:250.0pt'>
> <tr>
>  <td width=3D100 bgcolor=3D"#E8E8E8" =
>style=3D'width:50.0pt;background:#E8E8E8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span
>  style=3D'font-size:12.0pt'>&nbsp;</span></font></p>
>  </td>
>  <td width=3D400 bgcolor=3D"#E8E8E8" =
>style=3D'width:200.0pt;background:#E8E8E8;
>  padding:0in 0in 0in 0in'>
>  <p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span
>  style=3D'font-size:12.0pt'>&nbsp;</span></font></p>
>  </td>
> </tr>
></table>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Algu=E9m se habilita a demonstrar que</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; int[Sen(x)/(1+x), x] =3D Si(x+1)Cos(1) - =
>Ci(x+1)Sen(1)</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Si: Seno integral</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Ci: Cosseno integral</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Estas integrais s=E3o definidas para todo x complexo =
></span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; como segue</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Si(t) =3D int[Sen(t)/t, t=3D0..x]</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Ci(t) =3D gamma + ln(x) + int[(Cos(t)-1)/t, =
>t=3D0..x]</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Obrigado, desde j=E1.</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; =
>_______________________________________________________________________</=
>span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Yahoo! GeoCities</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Tudo para criar o seu site: ferramentas f=E1ceis de usar, =
>espa=E7o de
>sobra e acess=F3rios.</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; http://br.geocities.yahoo.com/</span></font></p>
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><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt;
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D</sp=
>an></font></p>
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><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; Instru=E7=F5es para entrar na lista, sair da lista e usar a =
>lista em</span></font></p>
>
></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; =
>http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html</span></font></p>
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></div>
>
><div>
>
><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
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>12.0pt'>&gt;
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D</sp=
>an></font></p>
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></div>
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><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
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>
><div>
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><p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
>style=3D'font-size:
>12.0pt'>&gt; </span></font></p>
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>
></body>
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>
>------=_NextPart_000_0022_01C32F3D.395FB530--
>=========================================================================
>Instrugues para entrar na lista, sair da lista e usar a lista em
>http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html
>=========================================================================

=========================================================================
Instruš§es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html
=========================================================================