📄 ch11_3_2.htm
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<TITLE> 积分 </TITLE>
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<H1>11.3.2 积分</H1>
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<FONT COLOR=#FF0000 FACE="Times New Roman">int</FONT>函数用以演算一函数的积分项，<FONT FACE="Times New Roman">
</FONT>这个函数要找出一符号式<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 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：
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<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
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<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
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<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
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<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
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<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
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我们示范几个例子：
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<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>
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<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>
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<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">;
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>int(S1)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">3/2*x^4-4/3*x^3+1/2*b*x^2-5*x</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>int(S2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">-cos(a)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>int(S3)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">2/3*x^(3/2)</FONT>
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<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>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">2/3*b^(3/2)- 2/3*a^(3/2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>int(S3,0.5,0.6)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">2/25*15^(1/2)-1/6*2^(1/2)</FONT>
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<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
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">0.0741<BR>
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