这个三角函数积分结果为复数，为什么？ - MATLAB爱好者论坛-LabFans.com

liu16 · 2009-08-25, 08:37

In[27]:= fs[x]

Out[27]= -1. If[
Cos[x] \[NotElement] Reals ||
0 <= Re[Cos[x]] <=
1.0125, (-1.04621*10^7 +
196.649 I) + (30773.6 - 28700. Cos[3. x] + 15166.2 Cos[4. x] -
6279.32 Cos[5. x] + 1796.76 Cos[6. x] - 253.512 Cos[7. x] +
41498.6 Log[Cos[x]] - 42086.1 Cos[3. x] Log[Cos[x]] +
24091.4 Cos[4. x] Log[Cos[x]] - 11256.5 Cos[5. x] Log[Cos[x]] +
4081.69 Cos[6. x] Log[Cos[x]] - 1014.05 Cos[7. x] Log[Cos[x]] +
125.191 Cos[8. x] Log[Cos[x]] +
Cos[2. x] (44206.2 + 61633.6 Log[Cos[x]] -
61633.6 Log[-1.0125 + 1. Cos[x]]) -
41498.6 Log[-1.0125 + 1. Cos[x]] +
42086.1 Cos[3. x] Log[-1.0125 + 1. Cos[x]] -
24091.4 Cos[4. x] Log[-1.0125 + 1. Cos[x]] +
11256.5 Cos[5. x] Log[-1.0125 + 1. Cos[x]] -
4081.69 Cos[6. x] Log[-1.0125 + 1. Cos[x]] +
1014.05 Cos[7. x] Log[-1.0125 + 1. Cos[x]] -
125.191 Cos[8. x] Log[-1.0125 + 1. Cos[x]] + (0. + 0. I) Sin[
x] + (0. + 0. I) Log[Cos[x]] Sin[
x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[x] +
Cos[
x] (-56644.5 - 77073.9 Log[Cos[x]] +
77073.9 Log[-1.0125 +
1. Cos[x]] + ((0. + 0. I) + (0. + 7.11628*10^-12 I) Log[
Cos[x]]) Sin[x]) + (0. + 0. I) Log[-1.0125 +
1. Cos[x]] Sin[2. x] + (0. + 0. I) Sin[
3. x] + (0. + 0. I) Log[Cos[x]] Sin[
3. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[
3. x] + (0. + 0. I) Sin[4. x] + (0. + 0. I) Log[Cos[x]] Sin[
4. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[
4. x] + (0. + 0. I) Sin[5. x] + (0. + 0. I) Log[Cos[x]] Sin[
5. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[
5. x] + (0. + 0. I) Sin[6. x] + (0. + 0. I) Log[Cos[x]] Sin[
6. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[
6. x] + (0. + 0. I) Sin[7. x] + (0. + 0. I) Log[Cos[x]] Sin[
7. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[
7. x] + (0. + 0. I) Log[Cos[x]] Sin[
8. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[
8. x])/(662.966 + 984.634 Cos[2. x] - 672.351 Cos[3. x] +
384.875 Cos[4. x] - 179.83 Cos[5. x] + 65.2075 Cos[6. x] -
16.2 Cos[7. x] + 2. Cos[8. x] +
Cos[x] (-1231.3 + (0. + 1.13687*10^-13 I) Sin[x]) + (0. +
0. I) Sin[x] + (0. + 0. I) Sin[3. x] + (0. + 0. I) Sin[
4. x] + (0. + 0. I) Sin[5. x] + (0. + 0. I) Sin[
6. x] + (0. + 0. I) Sin[7. x] + (0. + 0. I) Sin[8. x]),
Integrate[1/((1.0125 - 1. u)^5 u^5), {u, 1, Cos[x]},
Assumptions -> ! (Cos[x] \[NotElement] Reals ||
0 <= Re[Cos[x]] <= 1.0125)]]

In[28]:= fs[1]

Out[28]= 1.04621*10^7 + 3.1789*10^-6 I

In[29]:= fs[0]

Out[29]= 0

In[30]:= fs[.5]

Out[30]= 1.04601*10^7 + 3.17872*10^-6 I

2009-08-25, 08:37	#2
liu16 初级会员注册日期: 2009-07-30 帖子: 6 声望力: 0	回复: 这个三角函数积分结果为复数，为什么？ In[27]:= fs[x] Out[27]= -1. If[ Cos[x] \[NotElement] Reals \|\| 0 <= Re[Cos[x]] <= 1.0125, (-1.0462110^7 + 196.649 I) + (30773.6 - 28700. Cos[3. x] + 15166.2 Cos[4. x] - 6279.32 Cos[5. x] + 1796.76 Cos[6. x] - 253.512 Cos[7. x] + 41498.6 Log[Cos[x]] - 42086.1 Cos[3. x] Log[Cos[x]] + 24091.4 Cos[4. x] Log[Cos[x]] - 11256.5 Cos[5. x] Log[Cos[x]] + 4081.69 Cos[6. x] Log[Cos[x]] - 1014.05 Cos[7. x] Log[Cos[x]] + 125.191 Cos[8. x] Log[Cos[x]] + Cos[2. x] (44206.2 + 61633.6 Log[Cos[x]] - 61633.6 Log[-1.0125 + 1. Cos[x]]) - 41498.6 Log[-1.0125 + 1. Cos[x]] + 42086.1 Cos[3. x] Log[-1.0125 + 1. Cos[x]] - 24091.4 Cos[4. x] Log[-1.0125 + 1. Cos[x]] + 11256.5 Cos[5. x] Log[-1.0125 + 1. Cos[x]] - 4081.69 Cos[6. x] Log[-1.0125 + 1. Cos[x]] + 1014.05 Cos[7. x] Log[-1.0125 + 1. Cos[x]] - 125.191 Cos[8. x] Log[-1.0125 + 1. Cos[x]] + (0. + 0. I) Sin[ x] + (0. + 0. I) Log[Cos[x]] Sin[ x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[x] + Cos[ x] (-56644.5 - 77073.9 Log[Cos[x]] + 77073.9 Log[-1.0125 + 1. Cos[x]] + ((0. + 0. I) + (0. + 7.1162810^-12 I) Log[ Cos[x]]) Sin[x]) + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[2. x] + (0. + 0. I) Sin[ 3. x] + (0. + 0. I) Log[Cos[x]] Sin[ 3. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[ 3. x] + (0. + 0. I) Sin[4. x] + (0. + 0. I) Log[Cos[x]] Sin[ 4. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[ 4. x] + (0. + 0. I) Sin[5. x] + (0. + 0. I) Log[Cos[x]] Sin[ 5. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[ 5. x] + (0. + 0. I) Sin[6. x] + (0. + 0. I) Log[Cos[x]] Sin[ 6. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[ 6. x] + (0. + 0. I) Sin[7. x] + (0. + 0. I) Log[Cos[x]] Sin[ 7. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[ 7. x] + (0. + 0. I) Log[Cos[x]] Sin[ 8. x] + (0. + 0. I) Log[-1.0125 + 1. Cos[x]] Sin[ 8. x])/(662.966 + 984.634 Cos[2. x] - 672.351 Cos[3. x] + 384.875 Cos[4. x] - 179.83 Cos[5. x] + 65.2075 Cos[6. x] - 16.2 Cos[7. x] + 2. Cos[8. x] + Cos[x] (-1231.3 + (0. + 1.1368710^-13 I) Sin[x]) + (0. + 0. I) Sin[x] + (0. + 0. I) Sin[3. x] + (0. + 0. I) Sin[ 4. x] + (0. + 0. I) Sin[5. x] + (0. + 0. I) Sin[ 6. x] + (0. + 0. I) Sin[7. x] + (0. + 0. I) Sin[8. x]), Integrate[1/((1.0125 - 1. u)^5 u^5), {u, 1, Cos[x]}, Assumptions -> ! (Cos[x] \[NotElement] Reals \|\| 0 <= Re[Cos[x]] <= 1.0125)]] In[28]:= fs[1] Out[28]= 1.0462110^7 + 3.178910^-6 I In[29]:= fs[0] Out[29]= 0 In[30]:= fs[.5] Out[30]= 1.0460110^7 + 3.17872*10^-6 I