问一道简单的积分$sin(x^2)dx=？？？
（用$代表不定积分符号）[紫羊 (4-12 1:14, Long long ago)]
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x/2-(sin2x)/4use sin(x^2)=1/2(1-cos2x)[eternal_flame (4-12 1:28, Long long ago)] [ 传统版 | sForum ][登录后回复]2楼
(引用 eternal_flame:x/2-(sin2x)/4use sin(x^2)=1/2(1-cos2x))大哥：sin(x)*sin(x)才等于1/2(1-cos2x)[homeless (4-12 1:45, Long long ago)] [ 传统版 | sForum ][登录后回复]3楼
come:I could tell you last semester but now i forget to how to deal with it. Haha, sorry about it!!![homeless (4-12 1:46, Long long ago)] [ 传统版 | sForum ][登录后回复]4楼
No one uses LaTeX for math symbols?[Flying (4-12 2:09, Long long ago)] [ 传统版 | sForum ][登录后回复]5楼
(引用 Flying:No one uses LaTeX for math symbols?
...)Source code:<math width="200" height="300">
<param name="equation" value="\int\sin x^2 dx" />
</math>
(remember to choose "Use Huasing Code")[Flying (4-12 2:10, Long long ago)]
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(引用 homeless:come:I could tell you last semester but now i forget to how to deal with it. Haha, sorry about it!!!)这个可解么?佩服佩服[杨明 (4-12 2:31, Long long ago)] [ 传统版 | sForum ][登录后回复]7楼
个人感觉: 没有简单代数精确解尝试用taylor series（不急得是不是这个名字了）打开，然后逐项积分。所以我猜没有精确代数解。[杨明 (4-12 2:36, Long long ago)] [ 传统版 | sForum ][登录后回复]8楼
matlab says...>> syms x
>> y=sin(x^2)
y =
sin(x^2)
>> int(y)
ans =
1/2*2^(1/2)*pi^(1/2)*FresnelS(2^(1/2)/pi^(1/2)*x)
>>
don't ask me what is "FresnelS()"[逃课专家 (4-12 3:12, Long long ago)]
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(引用 杨明:这个可解么?佩服佩服)9494[狂ft (4-12 8:57, Long long ago)] [ 传统版 | sForum ][登录后回复]10楼
(引用 逃课专家:matlab says...>> syms x >> y=sin(x^2) y = sin(x^2) >> int(y) ans = 1/2*2^(1/2)*pi^(1/2)*FresnelS(2^(1/2)/pi^(1/2)*x) )Hehehe... followed by Google bah...http://functions.wolfram.com/GammaBetaErf/FresnelS/[Flying (4-12 10:52, Long long ago)] [ 传统版 | sForum ][登录后回复]11楼
Mathematica givesIntegrate[Sin[x^2],x]= Sqrt[Pi/2]*FresnelS[Sqrt[Pi/2]*x]
Integrate[Sin[x^2],{x,-Infinity,Infinity}]= Sqrt[Pi/2][freeflying (4-12 13:23, Long long ago)]
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(引用 homeless:come:I could tell you last semester but now i forget to how to deal with it. Haha, sorry about it!!!)哈哈,这都可以![洋葱 (4-12 15:23, Long long ago)] [ 传统版 | sForum ][登录后回复]13楼
根据哈工大的数学教材这个函数好想属于积不出的.
这类函数还有$dx/lnx, $sin(x)dx/x, 虽然看起来很简单.不知道各位高手是怎么积出来的?都是一些看不懂的东东... [洋葱 (4-12 15:24, Long long ago)]
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(引用 洋葱:根据哈工大的数学教材这个函数好想属于积不出的. 这类函数还有$dx/lnx, $sin(x)dx/x, 虽然看起来很简单.不知道各位高手是怎么积出来的?都...)............[我行故我 (4-12 16:01, Long long ago)] [ 传统版 | sForum ][登录后回复]15楼
Exact AnswerIn indefinite integral, it is not integrable.
However in definite integral, by complex analysis,
\int_0^{\infty}\sin(x^2)dx=\sqrt{\pi}/(2\sqrt{2}).
BTW, the Fresnel integral is defined as
c(z)=\int_0^z\cos(\pi*t^2/2)dt.
So matlab and mathematica give solutions related with Fresnel integral.[赫连春水 (4-15 10:39, Long long ago)]
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可以这样么sin (x^2)的taylor series是可以求出来的啊，所以，如果是不定积分的话，就可以通过泰勒级数找到一种数列的表达方法，如果是定积分的话，如果有精确度的限制，就能够求出答案来。
[鬼 (4-16 19:29, Long long ago)]
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