[數學]一題積分的小問題

[數學]一題積分的小問題

toadfadfadf 於 星期二 十月 02, 2007 7:04 pm


請教一題積分  我在某個地方的觀念有點卡住
                                                                               
   1
 ∫   cos(2πft+π) cos(2πft) dt
   0
                                                                               
         1
=  1/2 ∫    cos(π) + cos(4πft + π) dt
         0
                                                                               
= - 1/2
                                                                               
                                                                               
                                                                               
                                                                               
我想問的是
                                                                               
  1
∫   cos(4πft + π)  dt   =  0
  0
                                                                               
                                                                               
這種積分是要怎麼積呢 ?
要考慮 π  還是不用考慮 π
                                                                               
如果要考慮π的話  答案應該不是 0 才對
                                                                               
要怎麼推出答案是 0 的結果
                                                                               
希望有好心人解答一下
                                                                               
謝謝  ^^
 

toadfadfadf
訪客
 

Re: [數學]一題積分的小問題

G@ry 於 星期五 十月 05, 2007 12:18 am


toadfadfadf 寫到:
請教一題積分  我在某個地方的觀念有點卡住
                                                                               
   1
 ∫   cos(2πft+π) cos(2πft) dt
   0
                                                                               
         1
=  1/2 ∫    cos(π) + cos(4πft + π) dt
         0
                                                                               
= - 1/2
                                                                               
                                                                               
                                                                               
                                                                               
我想問的是
                                                                               
  1
∫   cos(4πft + π)  dt   =  0
  0
                                                                               
                                                                               
這種積分是要怎麼積呢 ?
要考慮 π  還是不用考慮 π
                                                                               
如果要考慮π的話  答案應該不是 0 才對
                                                                               
要怎麼推出答案是 0 的結果
                                                                               
希望有好心人解答一下
                                                                               
謝謝  ^^
 


  1
∫   cos(4πft + π)  dt
  0
    1
=∫   cos( (4ft+1)π )  dt   =  0,  if f∈Z
    0

因為 ∫ cos( uπ ) du =0, , f∈Z
☆子 是也

G@ry
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