Integración directa
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<div> <B>Propiedades</B></div> <div> <A HREF="id29_m.htm#p1_1" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad1</B></U></A></div> <div> <A HREF="id29_m.htm#p2" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad2</B></U></A></div> <div> <A HREF="id29_m.htm#p3" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad3</B></U></A></div> <div> <A HREF="id29_m.htm#p4" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad4</B></U></A></div> <div> <A HREF="id29_m.htm#p5a" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad5</B></U></A></div> <div> <A HREF="id29_m.htm#p6" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad6</B></U></A></div> <div> <A HREF="id29_m.htm#p7" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad7</B></U></A></div> <div> <A HREF="id29_m.htm#p8" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad8</B></U></A></div> <div> <A HREF="id29_m.htm#p9" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad9</B></U></A></div> <div> <A HREF="id29_m.htm#p10" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad10</B></U></A></div> <div> <A HREF="id29_m.htm#p11" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad11</B></U></A></div> <div> <A HREF="id29_m.htm#p12" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad12</B></U></A></div> <div> <A HREF="id29_m.htm#p13" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad13</B></U></A></div> <div> <A HREF="id29_m.htm#p14" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad14</B></U></A></div> <div> <A HREF="id29_m.htm#p15" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad15</B></U></A></div> <div> <A HREF="id29_m.htm#p16" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad16</B></U></A></div> <div> <A HREF="id29_m.htm#p17" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad17</B></U></A></div> <div> <A HREF="id29_m.htm#p18" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad18</B></U></A></div> <div> <A HREF="id29_m.htm#p19" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad19</B></U></A></div> <div> <A HREF="id29_m.htm#p20" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad20</B></U></A></div> <div> <A HREF="id29_m.htm#p21" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad21</B></U></A></div> <div> <A HREF="id29_m.htm#p22" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad22</B></U></A></div> <div> <A HREF="id29_m.htm#p23" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad23</B></U></A></div> <div> <A HREF="id29_m.htm#p24" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad24</B></U></A></div> <div> <A HREF="id29_m.htm#25" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Propiedad25</B></U></A></div> <bR> </td> <td valign="top" height=382 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <A NAME="integración_directa"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>Integración directa</B></div> <div> <FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>D</B></FONT><I>e cada regla de derivación se puede deducir una regla correspondiente de integración</I>. La integración directa es aplicable cuando identificamos la función primitiva de forma inmediata; esto es, cuando conocemos la regla de derivación que al aplicarla nos permite hallar el integrando a partir de la función primitiva.</div> <div> Ejemplo: </div> <div> <IMG SRC="3410c1d0.gif" border=0 width="268" height="29" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="595" BORDERCOLORLIGHT="#009900" BORDERCOLORDARK="#33FFCC" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=2 BGCOLOR=#00CC99 HEIGHT= 39 WIDTH="579"><div> <A NAME="propiedades_fundamentales_de_la"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#FF0099" FACE="Times New Roman" ><B>Propiedades fundamentales de la antidiferenciación</B></FONT></div> <bR> </tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 55 ><NOBR><div> <A NAME="p1_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="3423c1d0.gif" border=0 width="316" height="29" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> Esta propiedad indica que podemos sacar un factor <I><B>constante</B></I> de la integral.</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 63 ><NOBR><div> <A NAME="p2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="34390380.gif" border=0 width="400" height="56" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 87 ><NOBR><div> <A NAME="p3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="34437500.gif" border=0 width="567" height="80" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 60 ><NOBR><div> <A NAME="p4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0f4eb350.gif" border=0 width="235" height="53" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="271"><div> <A NAME="p5a"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0f5691d0.gif" border=0 width="105" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 68 ><NOBR><div> <A NAME="p6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0f6dd3d0.gif" border=0 width="477" height="61" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 46 ><NOBR><div> <A NAME="p7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0f7d1270.gif" border=0 width="209" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="271"><div> <A NAME="p8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0f87f1d0.gif" border=0 width="127" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 68 WIDTH="305"><div> <A NAME="p9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0f9b41d0.gif" border=0 width="180" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> <tD VALIGN=TOP><NOBR><div> <A NAME="p10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0faef3d0.gif" border=0 width="239" height="61" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 36 WIDTH="305"><div> <A NAME="p11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0fbb41d0.gif" border=0 width="180" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> <tD VALIGN=TOP WIDTH="271"><div> <A NAME="p12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0fca81d0.gif" border=0 width="168" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 36 WIDTH="305"><div> <A NAME="p13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0fdb01d0.gif" border=0 width="176" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> <tD VALIGN=TOP><NOBR><div> <A NAME="p14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0febb1d0.gif" border=0 width="187" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 36 ><NOBR><div> <A NAME="p15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="0ffc91d0.gif" border=0 width="201" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A NAME="p16"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="100d41d0.gif" border=0 width="212" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 52 ><NOBR><div> <A NAME="p17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="101c82d0.gif" border=0 width="200" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A NAME="p18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="102bd280.gif" border=0 width="189" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 52 ><NOBR><div> <A NAME="p19"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="103d12d0.gif" border=0 width="209" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A NAME="p20"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="104b81d0.gif" border=0 width="184" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 36 WIDTH="305"><div> <A NAME="p21"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="105b81d0.gif" border=0 width="184" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> <tD VALIGN=TOP><NOBR><div> <A NAME="p22"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="106c01d0.gif" border=0 width="192" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 36 ><NOBR><div> <A NAME="p23"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="107c91d0.gif" border=0 width="201" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A NAME="p24"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="108eb1d0.gif" border=0 width="235" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 36 ><NOBR><div> <A NAME="25"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="109eb1d0.gif" border=0 width="235" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="271"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="36" ALIGN="bottom" WIDTH="271" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="612" BORDERCOLORLIGHT="#00FFFF" BORDERCOLORDARK="#0000FF" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=3 BGCOLOR=#00CCCC HEIGHT= 58 WIDTH="600"><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> <B> </B><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>E</B></FONT><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >fectúe las operaciones de antidiferenciación que se indican, aplicando las propiedades correspondientes en cada caso:</FONT></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 50 WIDTH="198"><div> <A HREF="#1__" TITLE="Integración directa"><U><IMG SRC="10a601d0.gif" border=0 width="96" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#2__" TITLE="Integración directa"><U><IMG SRC="10ba71d0.gif" border=0 width="167" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#3__" TITLE="Integración directa"><U><IMG SRC="10c912b0.gif" border=0 width="145" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 47 ><NOBR><div> <A HREF="#4__" TITLE="Integración directa"><U><IMG SRC="10d9b1d0.gif" border=0 width="155" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#5__" TITLE="Integración directa"><U><IMG SRC="10e6d1d0.gif" border=0 width="109" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#6__" TITLE="Integración directa"><U><IMG SRC="10f7b280.gif" border=0 width="123" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 50 WIDTH="198"><div> <A HREF="#7__" TITLE="Integración directa"><U><IMG SRC="11080270.gif" border=0 width="128" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#8" TITLE="Integración directa"><U><IMG SRC="1114d2b0.gif" border=0 width="77" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#9" TITLE="Integración directa"><U><IMG SRC="11260280.gif" border=0 width="96" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 42 WIDTH="198"><div> <A HREF="#10" TITLE="Integración directa"><U><IMG SRC="4b350230.gif" border=0 width="80" height="35" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="42" ALIGN="bottom" WIDTH="198" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="198"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="42" ALIGN="bottom" WIDTH="198" HSPACE="0" VSPACE="0"></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>1.</B></FONT><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B> </B></FONT>Solución:</div> <div> <IMG SRC="1138f6d0.gif" border=0 width="399" height="109" ALT="MathType 5.0 Equation" 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><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>2.</B></FONT><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B> </B></FONT>Solución:</div> <div> <IMG SRC="114545d0.gif" border=0 width="596" height="93" ALT="MathType 5.0 Equation" 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><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>3.</B></FONT><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B> </B></FONT>Solución:</div> <div> <IMG SRC="11575c50.gif" border=0 width="629" height="197" ALT="MathType 5.0 Equation" 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><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>4.</B></FONT><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B> </B></FONT>Solución:</div> <div> <IMG SRC="116b3a80.gif" border=0 width="435" height="168" ALT="MathType 5.0 Equation" 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><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>5.</B></FONT><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B> </B></FONT>Solución:</div> <div> <IMG SRC="117bbe40.gif" border=0 width="443" height="228" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></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="#CC0033" FACE="Times New Roman" ><B>6.</B></FONT><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B> </B></FONT>Solución:</div> <div> <IMG SRC="11815d30.gif" border=0 width="533" height="211" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></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="#CC0033" FACE="Times New Roman" ><B>7.</B></FONT><FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B> </B></FONT>Solución:</div> <div> <IMG SRC="1192fcc0.gif" border=0 width="559" height="204" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B><IMG SRC="11a4d2b0.gif" border=0 width="77" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <div> <B><IMG SRC="11bac700.gif" border=0 width="428" height="112" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B><IMG SRC="11c60280.gif" border=0 width="96" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <div> <B><IMG SRC="11d61690.gif" border=0 width="353" height="105" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="4b450230.gif" border=0 width="80" height="35" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="4b5e7430.gif" border=0 width="487" height="67" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <bR> <bR> </td> <td valign="top" rowspan="2" width=14 BGCOLOR="#009999" TEXT="#080000"> <bR> </td> </tr><tr> <td valign="top" height=21 BGCOLOR="#009999" TEXT="#080000"> <div> <B>| </B><A HREF="id29_m.htm#integración_directa" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Arriba</B></U></A><B> | </B><A HREF="id29_m.htm#ejercicios_resueltos" TARGET="TRLX_Middle" TITLE="Integración directa"><U><B>Ejercicios resueltos</B></U></A><B> |</B></div> </td> </tr></table></body>