问一个积分的问题

fishell718

我想在圆心在（根号2/2，根号2/2），半径为1的圆内做一个关于三角函数的积分，编写了如下代码：
syms theta r;
syms f1 df y1 y2;
PI=3.1415926;
f1=2*cos(theta/2)*cos(3*theta/2)+3*sin(theta).^2*(cos(theta)+cos(3*theta/2)*cos(5*theta/2));%积分表达式
df=r^(-2)*f1/4/PI;
df=subs(df);
y1=subs(int(df,'r'));
r=(cos(theta)+sin(theta))*2.^(0.5);%定义积分范围，即圆的极坐标方程
y1=subs(y1);
y2=int(y1,'theta',0,2*PI)
但是这样计算得到的y2值为NaN，不知道该怎么办了，请赐教

Walker0728

你仔细检查一下你的程序，不知道是怎么回事我把你的程序用我的matlab运行时无法响应，根本不是你说的得到一个NaN;我看你下你的程序觉得是subs函数应用的有问题，你看看帮助文档

chenxin168

n(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6+650*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4+650*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4+4000*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6+4000*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4+2000*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8-60*atanh(1/2*(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)-1)*2^(1/2))-60*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))+650*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4+65*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10+2000*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4-325*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8-65*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-650*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6+65*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10+325*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8+650*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6+65*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10+325*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8-650*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4+400*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4+40*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10+200*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8+400*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6+400*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4+200*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2+200*2^(1/2)*atan(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2+5300*2^(1/2)*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^7*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8+1060*2^(1/2)*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^7*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-650*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6-650*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4-65*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-325*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8-650*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)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atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)-1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6-3000*atanh(1/2*(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)-1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6-1500*atanh(1/2*(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)-1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-3000*atanh(1/2*(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)-1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4-1500*atanh(1/2*(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)-1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8-260*2^(1/2)*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10+60*2^(1/2)*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-1580*2^(1/2)*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-320*2^(1/2)*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-60*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-6000*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6-3000*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8-600*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-1500*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-3000*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4-3000*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6-1500*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8-300*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10-300*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-600*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^4-600*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^6-300*atanh(1/2*(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)+1)*2^(1/2))*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^10*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^8+325*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1-2*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))*tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-65*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2-1+2*tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta))-65*2^(1/2)*log(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2+1)+65*2^(1/2)*log(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2+1)+40*2^(1/2)*atan(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)))/(tan(-atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2+1)^5/(tan(atan(1/2*(2^(1/2)-2)*2^(1/2))+1/2*theta)^2+1)^5,theta = 0,right)-6556968033891067619864383324160*2^(1/2)*log(-tan(3537118815677477/1125899906842624)^2+1+2*tan(3537118815677477/1125899906842624))-12676506002282293962583006632005*2^(1/2)+504382156453159047681875640320*2^(1/2)*pi)/(1+tan(3537118815677477/1125899906842624)^2)^5

chenxin168

怎么计算出这个结果呀？

fishell718

我又试了一下，还是NaN啊。我用的MATLAB7.1版本。另外，我是直接把代码输入到命令行的，没有用.m文件

2# Walker0728

fishell718

汗，难道每个人运算的结果都不同。。。

4# chenxin168

messenger

应该是Matlab版本不同，符号引掣不同，结果不同。

qibbxxt

我计算出来是NaN,不知道你计算结果用于做什么，如果最后的结果是数值的话，可以用数值积分

fishell718

恩，是的，已经用数值积分完成了，非常感谢！

8# qibbxxt

feigo

感觉积分范围好像有点问题，最后的结果应该是数值吧？