📄 第三节用mathematica作积分计算.htm

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src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image028.wmz"></V:SHAPE><![endif]--><IMG src="images/3.htm87.gif"       
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does not converge on{0, 1}.</font></b></SPAN></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN       
lang=EN-US><font size="4"><b>Out[4]=(Integrate[<SPAN style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1040      
style="HEIGHT: 30.75pt; WIDTH: 12pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA      
o:title=""      
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image028.wmz"></V:SHAPE><![endif]--><IMG src="images/3.htm88.gif"      
v:shapes="_x0000_i1040" width="16" height="41"></SPAN><!--[if gte mso 9]><xml>     
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1040"     
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, {x, 0, 1}, Assumptions -&gt; -1]<SPAN       
style="mso-spacerun: yes">&nbsp;&nbsp;</SPAN></b></font></SPAN></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN       
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">上述输出表明</font></b></SPAN><b><font size="4"><SPAN      
lang=EN-US>n=1</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">时，虽然可以算出却输入并不是最简的格式；</SPAN><SPAN      
lang=EN-US>n=-1</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">时，无法计算，原样输出。</SPAN></font></b></P>     
<P class=MsoNormal style="line-height: 200%"><font size="4"><b><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">例</SPAN><SPAN      
lang=EN-US>2 </SPAN><SPAN       
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">求下列定积分</SPAN></b></font></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b><SPAN      
style="mso-text-raise: -60.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1041      
style="HEIGHT: 138.75pt; WIDTH: 215.25pt" o:ole=""      
type="#_x0000_t75"><V:IMAGEDATA o:title=""      
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image031.wmz"></V:SHAPE><![endif]--><IMG src="images/3.htm89.gif"      
v:shapes="_x0000_i1041" width="287" height="185"></SPAN><!--[if gte mso 9]><xml>     
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1041"     
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</b></font>      
</SPAN></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><b>解：</b></font></SPAN></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">（</SPAN><SPAN      
lang=EN-US>1</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN      
lang=EN-US>In[1]:=Integrate[x^2Cos[x], {x, 0, 2*Pi}]</SPAN></b></font></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>&nbsp;&nbsp; 
</b></font>      
</SPAN><font size="4"><b><SPAN      
lang=EN-US>Out[1]=4</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">π</SPAN></b></font></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN      
lang=EN-US>2</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN      
lang=EN-US>In[2]:=Integrate[ArcCos[x], {x, 0, 1}]</SPAN></font></b></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>&nbsp;&nbsp; 
Out[2]=1</b></font>      
</SPAN></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN      
lang=EN-US>3</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN      
lang=EN-US>In[3]:=Integrate[(E^x - 1)^(1/2), {x, 0, ln2}]</SPAN></font></b></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>Out[3]=<SPAN      
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1042      
style="HEIGHT: 21pt; WIDTH: 177pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA      
o:title=""      
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image033.wmz"></V:SHAPE><![endif]--><IMG src="images/3.htm90.gif"      
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</b></font>      
</SPAN></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN      
lang=EN-US>4</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN      
lang=EN-US>In[4]:=Integrate[1/(1 + x^2), {x, -Infinity, Infinity}]</SPAN></font></b></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>&nbsp;&nbsp; 
</b></font>      
</SPAN><font size="4"><b><SPAN lang=EN-US>Out[4]=       
</SPAN><SPAN       
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">π</SPAN></b></font></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN       
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN      
lang=EN-US>5</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN      
lang=EN-US>In[5]:=Integrate[(x*Sin[x])^2, {x, 0, Pi}]</SPAN></font></b></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>&nbsp;&nbsp; 
Out[5]=<SPAN      
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1043      
style="HEIGHT: 33pt; WIDTH: 48.75pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA      
o:title=""      
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image035.wmz"></V:SHAPE><![endif]--><IMG src="images/3.htm91.gif"      
v:shapes="_x0000_i1043" width="65" height="44"></SPAN><!--[if gte mso 9]><xml>     
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</b></font>      
</SPAN></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN      
lang=EN-US>6</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN      
lang=EN-US>In[6]:=Integrate[x(2 - x^2)^12, {x, 0, 1}]</SPAN></font></b></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>&nbsp;&nbsp; 
Out[6]=<SPAN      
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1044      
style="HEIGHT: 30.75pt; WIDTH: 27.75pt" o:ole="" type="#_x0000_t75">      
<V:IMAGEDATA o:title=""      
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image037.wmz"></V:SHAPE><![endif]--><IMG src="images/3.htm92.gif"      
v:shapes="_x0000_i1044" width="37" height="41"></SPAN><!--[if gte mso 9]><xml>     
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1044"     
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</b></font>      
</SPAN></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN      
lang=EN-US>7</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN      
lang=EN-US>In[7]:=Integrate[x + y, {x, 0, 1}, {y, 0, 1}]</SPAN></font></b></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>&nbsp;&nbsp; 
Out[7]=1</b></font>      
</SPAN></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN      
lang=EN-US>8</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN      
lang=EN-US>In[8]:=Integrate[x*y^2, {x, 0, 1}, {y, x^2, x}]</SPAN></font></b></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>&nbsp;&nbsp; 
Out[8]=<SPAN      
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1045      
style="HEIGHT: 30.75pt; WIDTH: 18pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA      
o:title=""      
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image039.wmz"></V:SHAPE><![endif]--><IMG src="images/3.htm93.gif"      
v:shapes="_x0000_i1045" width="24" height="41"></SPAN></b></font><!--[if gte mso 9]><xml>     
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</SPAN></P>     
     
<p class="MsoNormal" style="text-indent: 17.95pt; line-height: 200%">　</p>
<p class="MsoNormal" style="text-indent: 17.95pt; line-height: 200%">　</p>

<P align=center class=MsoNormal style="text-align: center; line-height: 200%"><span style="font-family: 宋体; mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><a href="index.htm">主目录</a></span><span style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">  
| <a href="第二节%20用Mathematica求极限和求微分.htm"></a> <a href="第一节%20Mathematica快速入门.htm">第一节</a>     
| <a href="第二节%20用Mathematica求极限和求微分.htm">第二节</a> | <a href="第三节%20用Mathematica作积分计算.htm">第三节</a>     
| <a href="第四节%20用Mathematica解方程和作级数运算.htm">第四节</a>     
| <a href="第四节%20用Mathematica解方程和作级数运算.htm">第五节</a>     
| <a href="第六节%20Mathematica编程基础.htm">第六节</a></span></P>     
    
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📄 第三节 用mathematica作积分计算.htm

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📄 第三节用mathematica作积分计算.htm
