Teorema del valor medio para la integral definida

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=98 BGCOLOR="#006600" TEXT="#F7F7FF" bgproperties="fixed" background="05700732dwnpjk.jpg"> <div> <FONT SIZE="6" COLOR="#FFFFFF" FACE="Times New Roman" ><B>C á l c u l o   2 1</B></FONT><FONT SIZE="6" COLOR="#FFCC66" FACE="Arial" ><B> </B></FONT><FONT SIZE="2" COLOR="#FFFFCC" FACE="Arial" >   </FONT><B>  |   </B><A HREF="index.htm" TARGET="_top" TITLE="A n á l i s i s M a t e m á t i c o"><U><B>Home</B></U></A><B> |  </B><A HREF="id98.htm" TARGET="_top" TITLE=" | Contenido |"><U><B>Contenido</B></U></A><B> |  </B><A HREF="id341.htm" TARGET="_top" TITLE="Introducción al cálculo integral"><U><B>Cálculo integral</B></U></A><B> |</B></div> <div> <A HREF="id342.htm" TARGET="_top" TITLE="Área"><U>Área</U></A>   |   <A HREF="id344.htm" TARGET="_top" TITLE="La integral definida"><U>La integral definida</U></A>   |   <A HREF="id345.htm" TARGET="_top" 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valign="top" rowspan="2" width=119 BGCOLOR="#006600" TEXT="#F7F7FF"> <bR> <bR> <div> <A HREF="id346_m.htm#arriba" TARGET="TRLX_Middle" TITLE="Teorema del valor medio para la integral"><U><B> <img src="HTMLobj-5699/aniGif.gif" alt="arriba" border="0" align="bottom" width="50" height="50">  </B></U></A></div> </td> <td valign="top" height=361 colspan=2 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <U>Teorema del valor medio para la integral definida</U></div> <div>  <A NAME="arriba"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>La siguiente propiedad de la integral definida sirve de base para demostrar el Primer Teorema fundamental del cálculo. </div> <bR> <div> <B><IMG SRC="1632722a0.gif" border=0 width="626" height="298" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B><IMG SRC="1633473d0.gif" border=0 width="583" height="61" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <DIV ALIGN="LEFT"></DIV> <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> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="639" BORDERCOLORLIGHT="#33FFCC" BORDERCOLORDARK="#009900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 291 WIDTH="631"><div> <B><IMG SRC="1634724b0.gif" border=0 width="626" height="75" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <FONT SIZE="3" COLOR="#9900FF" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >3</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >6</FONT>, utilice le Teorema del valor medio para la integral definida, <FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" >PID11</FONT>, para demostrar la desigualdad dada.</div> <div> <A HREF="#1" TITLE="Teorema del valor medio para la integral"><U><IMG SRC="163545270.gif" border=0 width="69" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>              <A HREF="#2" TITLE="Teorema del valor medio para la integral"><U><IMG SRC="163669270.gif" border=0 width="105" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>              <A HREF="#3" TITLE="Teorema del valor medio para la integral"><U><IMG SRC="16377f270.gif" border=0 width="127" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>              <A HREF="#4" TITLE="Teorema del valor medio para la integral"><U><IMG SRC="16387f270.gif" border=0 width="127" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#5" TITLE="Teorema del valor medio para la integral"><U><IMG SRC="163993270.gif" border=0 width="147" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>               <A HREF="#6" TITLE="Teorema del valor medio para la integral"><U><IMG SRC="163a952b0.gif" border=0 width="149" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#7" TITLE="Teorema del valor medio para la integral"><U><IMG SRC="163b644f0.gif" border=0 width="612" height="79" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></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><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B><IMG SRC="163c73460.gif" border=0 width="627" height="326" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B><IMG SRC="163d72370.gif" border=0 width="626" height="311" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B><IMG SRC="163e9be00.gif" border=0 width="411" height="480" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <bR> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B><IMG SRC="163fefe50.gif" border=0 width="495" height="485" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <bR> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B><IMG SRC="1640f1f80.gif" border=0 width="497" height="504" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <bR> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B><IMG SRC="164133230.gif" border=0 width="563" height="547" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <bR> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B><IMG SRC="164272210.gif" border=0 width="626" height="289" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <bR> <bR> <bR> </td> </tr><tr> <td valign="top" colspan=2 height=21 BGCOLOR="#006600" TEXT="#F7F7FF"> <div> <A HREF="id346_m.htm#ejercicios_resueltos" TARGET="TRLX_Middle" TITLE="Teorema del valor medio para la integral"><U><B>Ejercicios resueltos</B></U></A></div> </td> </tr></table></body>