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<TITLE> 二次函数法 </TITLE>
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<H1>9.1.2 二次函数法</H1>
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<FONT FACE="Times New Roman">MATLAB </FONT>另外提供二种积分函数，它们分别是辛普森法<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">quad</FONT><FONT FACE="Times New Roman">
</FONT>和牛顿<FONT FACE="Times New Roman">-</FONT>康兹法<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">quad8</FONT>。三种方法的精确度由低
而高，分别为<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">trapz</FONT><FONT FACE="Times New Roman">,</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">
quad</FONT><FONT FACE="Times New Roman">,</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">
quad8</FONT>。<BR>
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由于这二种方法依据的积分法不同于梯形法，因此它们的语法就和<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">trapz</FONT><FONT FACE="Times New Roman">
</FONT>不同；其语法为<FONT FACE="Times New Roman"> </FONT><FONT COLOR=#FF0000 FACE="Times New Roman">quad('function',a,b)</FONT>
（<FONT COLOR=#FF0000 FACE="Times New Roman">quad8</FONT>语法相同），其中<FONT COLOR=#FF0000 FACE="Times New Roman">function</FONT>是一已定义函数的名称（如<FONT COLOR=#FF0000 FACE="Times New Roman">sin</FONT><FONT FACE="Times New Roman">,
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">cos</FONT><FONT FACE="Times New Roman">,
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">sqrt</FONT><FONT FACE="Times New Roman">,
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">log</FONT><FONT FACE="Times New Roman">
</FONT>等），而<FONT FACE="Times New Roman"> </FONT><FONT COLOR=#FF0000 FACE="Times New Roman">a</FONT><FONT FACE="Times New Roman">,
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">b</FONT>是积分的下限和
上限。和<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">trapz</FONT>比较，<FONT COLOR=#FF0000 FACE="Times New Roman">quad</FONT><FONT FACE="Times New Roman">,
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">quad8</FONT>不同之处在于这二者类似解析式的积分式，只须设定上下限及定义要积分
的函数；而<FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">trapz</FONT>则是针对离散点型态的数据做积分。
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我们看一简单积分式
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以下为<FONT FACE="Times New Roman"> MATLAB </FONT>的程式
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> a=0; b=0.5;</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> kq=quad('sqrt',a,b)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">kq =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 0.2357</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> kq8=quad8('sqrt',a,b)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">kq8 =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 0.2357<BR>
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再来看一个较复杂的积分式
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> x=-1:0.17:2;</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> y=humps(x);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> area=trapz(x,y)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">area =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 25.9174</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> x=-1:0.07:2;</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> y=humps(x);</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> area=trapz(x,y)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">area =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 26.6243</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> area=quad('hump',-1,2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">area =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 26.3450</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> area=quad8('hump',-1,2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">area =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 26.3450<BR>
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