Teoremas fundamentales del cálculo

<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> </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> Teoremas fundamentales del cálculo</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>  <A NAME="primer_teorema_fundamental_del_c_lculo"><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>Primer teorema fundamental del cálculo:</B></FONT></div> <div> <IMG SRC="20d0727c0.gif" border=0 width="626" height="124" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="segundo_teorema_fundamental_del_c_lculo"><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>Segundo teorema fundamental del cálculo:</B></FONT></div> <div> <IMG SRC="20d1724f0.gif" border=0 width="626" height="79" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="606" BORDERCOLORLIGHT="#33FFCC" BORDERCOLORDARK="#009900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 541 WIDTH="598"><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> <FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >1</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >14</FONT>, evalúe la integral definida. </div> <div> En los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >15</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >21</FONT>, calcule la derivada. </div> <div> <FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>Nota:</B></FONT> para resolver los ejercicios es necesario conocer algunas técnicas de integración, por el momento sólo es indispensable aprender la <A HREF="id468.htm" TARGET="_top" TITLE="Integración directa"><U>integración directa</U></A> y la <A HREF="id469.htm" TARGET="_top" TITLE="Integración por sustitución"><U>integración por sustitución</U></A>.</div> <bR> <div> <A HREF="#1" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20d28c270.gif" border=0 width="140" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                     <A HREF="#2" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20d377270.gif" border=0 width="119" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                   <A HREF="#3" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20d471290.gif" border=0 width="113" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#4" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20d577270.gif" border=0 width="119" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                          <A HREF="#5" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20d669270.gif" border=0 width="105" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                       <A HREF="#6" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20d784270.gif" border=0 width="132" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> </div> <div> <A HREF="#7" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20d85f2b0.gif" border=0 width="95" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                                <A HREF="#8" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20d96b270.gif" border=0 width="107" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                      <A HREF="#9" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20da85300.gif" border=0 width="133" height="48" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#10" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20db79270.gif" border=0 width="121" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                        <A HREF="#11" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20dc65270.gif" border=0 width="101" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                       <A HREF="#12" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20dd70270.gif" border=0 width="112" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#13" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20de90270.gif" border=0 width="144" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                  <A HREF="#14" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20dfc9270.gif" border=0 width="201" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#15" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20e081270.gif" border=0 width="129" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                      <A HREF="#16" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20e17b270.gif" border=0 width="123" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                 <A HREF="#17" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20e279270.gif" border=0 width="121" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#18" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20e397270.gif" border=0 width="151" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                <A HREF="#19" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20e484290.gif" border=0 width="132" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>               <A HREF="#20" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20e587270.gif" border=0 width="135" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#21" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20e687270.gif" border=0 width="135" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#22" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="20e729370.gif" border=0 width="553" height="55" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> </TABLE></div> <div> <B> </B></div> <DIV ALIGN="LEFT"></DIV> <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="20e8af100.gif" border=0 width="431" height="272" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></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><IMG SRC="20e93b1f0.gif" border=0 width="571" height="287" 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