Integrales impropias

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#006666" TEXT="#080000"> <div> <B>C á l c u l o   2 1</B><FONT SIZE="4" COLOR="#FFCC66" FACE="Bell MT" ><B> </B></FONT><FONT SIZE="4" COLOR="#FFFFCC" FACE="Bell MT" >   </FONT><B> </B> |   <A HREF="index.htm" TARGET="_top" TITLE="Cálculo 21"><U>Home</U></A>  |  <A HREF="id98.htm" TARGET="_top" TITLE="Contenido"><U>Contenido</U></A>  |  <A HREF="id341.htm" TARGET="_top" TITLE="Introducción al cálculo integral"><U>Cálculo integral</U></A>  |</div> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=160 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 colspan=2 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> Integrales impropias</div> <bR> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3926688482" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B> <A NAME="arriba_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>L</B></FONT>as denominadas <I>integrales impropias</I> son una clase especial de <I>integrales definidas</I> (integrales de Riemann) en las que el intervalo de integración o la función en el integrando o ambos presentan ciertas particularidades. </div> <div> <IMG SRC="236176670.gif" border=0 width="630" height="103" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="236272650.gif" border=0 width="626" height="357" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="236372500.gif" border=0 width="626" height="80" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> si los límites existen.</div> <bR> <div> <IMG SRC="236472e90.gif" border=0 width="626" height="233" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="2365727e0.gif" border=0 width="626" height="126" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <FONT SIZE="3" COLOR="#FF00FF" FACE="Times New Roman" ><B>C</B></FONT>uando los límites, en las definiciones anteriores, existen, se dice que la integral es <I>convergente</I>, en caso contrario, se dice que la integral es <I>divergente</I>.</div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="605" BORDERCOLORLIGHT="#33FFCC" BORDERCOLORDARK="#009900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 165 ><NOBR><div>  <A NAME="ejercicios_resueltos"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>Ejercicios resueltos</B></FONT></div> <bR> <div> <B>E</B><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >n los ejercicios </FONT>1<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" > a </FONT>5<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >, si la integral es convergente, evalúela.</FONT></div> <bR> <div> <A HREF="#1" TITLE="Integrales impropias"><U><IMG SRC="236651270.gif" border=0 width="81" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                            <A HREF="#2" TITLE="Integrales impropias"><U><IMG SRC="23676b290.gif" border=0 width="107" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                            <A HREF="#3" TITLE="Integrales impropias"><U><IMG SRC="23687b280.gif" border=0 width="123" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#4" TITLE="Integrales impropias"><U><IMG SRC="23695f280.gif" border=0 width="95" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                         <A HREF="#5" TITLE="Integrales impropias"><U><IMG SRC="236a70270.gif" border=0 width="112" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="597"><div> <FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>M</B></FONT><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >ás ejercicios resueltos:</FONT><B>  </B><B>Leithold 7.9</B><B>, </B><B>Leithold 7.10</B></div> </tD> </tR> </TABLE></div> <bR> <div> <B>S o l u c i o n e s </B></div> <bR> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="236b51270.gif" border=0 width="81" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="236c5a750.gif" border=0 width="602" height="117" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="236d6b290.gif" border=0 width="107" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="236e73730.gif" border=0 width="627" height="371" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="236f7b280.gif" border=0 width="123" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="23703be10.gif" border=0 width="571" height="481" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="237150280.gif" border=0 width="80" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="237226cd0.gif" border=0 width="550" height="205" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="237370270.gif" border=0 width="112" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="237448ad0.gif" border=0 width="584" height="173" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <bR> <bR> <bR> </td> </tr><tr> <td valign="top" colspan=2 height=24 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