📄 ch11_3_2.htm
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<title> 积分 </title>
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<font COLOR="#0000FF">
<h1>11.3.2 积分</h1>
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<p><font COLOR="#FF0000" FACE="Times New Roman">int</font>函数用以演算一函数的积分项，
这个函数要找出一符号式<font COLOR="#FF0000"> </font><font COLOR="#FF0000" FACE="Times New Roman">F </font>使得<font COLOR="#FF0000" FACE="Times New Roman">diff(F)=f</font>。如果积分式的解析式
<font FACE="Times New Roman">(analytical form, closed form) </font>不存在的话或是MATLAB无法找到，则<font COLOR="#FF0000"> </font><font COLOR="#FF0000" FACE="Times New Roman">int </font>传回原输入的符号式。相关的函数语法有下列
4个： </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">int(f)</font> 传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对预设独立变数的积分值 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">int(f,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">t</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">)</font> 传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对独立变数<font COLOR="#FF0000" FACE="Times New Roman">t</font>的积分值
</p>
<p><font COLOR="#FF0000" FACE="Times New Roman">int(f,a,b)</font> 传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对预设独立变数的积分值，积分区间为<font COLOR="#FF0000" FACE="Times New Roman">[a,b]</font>，<font COLOR="#FF0000" FACE="Times New Roman">a</font>和<font COLOR="#FF0000" FACE="Times New Roman">b</font>为数值式
</p>
<p><font COLOR="#FF0000" FACE="Times New Roman">int(f,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">t</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">,a,b)</font> 传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对独立变数<font COLOR="#FF0000" FACE="Times New Roman">t</font>的积分值，积分区间为<font COLOR="#FF0000" FACE="Times New Roman">[a,b]</font>，<font COLOR="#FF0000" FACE="Times New Roman">a</font>和<font COLOR="#FF0000" FACE="Times New Roman">b</font>为数值式
</p>
<p><font COLOR="#FF0000" FACE="Times New Roman">int(f,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">m</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">n</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">)</font> 传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对预设变数的积分值，积分区间为<font COLOR="#FF0000" FACE="Times New Roman">[m,n]</font>，<font COLOR="#FF0000" FACE="Times New Roman">m</font>和<font COLOR="#FF0000" FACE="Times New Roman">n</font>为符号式
<br>
</p>
<p>我们示范几个例子： </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>S1 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">6*x^3-4*x^2+b*x-5</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">;</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>S2 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">sin(a)</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">;</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>S3 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">sqrt(x)</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">; <br>
</font></p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>int(S1)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">3/2*x^4-4/3*x^3+1/2*b*x^2-5*x</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>int(S2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">-cos(a)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>int(S3)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">2/3*x^(3/2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>int(S3,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">a</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">b</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">2/3*b^(3/2)- 2/3*a^(3/2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>int(S3,0.5,0.6)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">2/25*15^(1/2)-1/6*2^(1/2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>numeric(int(S3,0.5,0.6)) % </font>使用<font COLOR="#FF0000" FACE="Times New Roman">numeric</font>函数可以计算积分的数值 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">0.0741<br>
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