Integration: ∫3 dx - 3*∫dx

👨🏻‍🏫 學術台數學

babycatpriere

2006-10-20 11:56 am

Is the answer 0?
or 0 + C?
or something else...?

駛唔駛 "+C"？...
個答案好似係 0、因為 ∫3 dx = 3*∫dx
但唔+C又好似唔make sense...

更新1:

駛唔駛+C？... 個答案好似係 0、因為 ∫3 dx = 3*∫dx 但唔+C又好似唔make sense...

回答 (4)

myisland8132

2006-10-20 12:06 pm

✔ 最佳答案

∫3 dx - 3*∫dx

=∫3 dx - 3*∫1 dx

=3x+C1-3x-C2

=C1-C2

=C

應該加C

又

∫3 dx - 3*∫dx

=3*∫1 dx - 3*∫1 dx

=3(∫1 dx - ∫1 dx)

=3∫(1- 1) dx

=3C1

=C

2006-10-20 04:15:56 補充：
用文字說法就是因為不能肯定前面的常數等於後面的常數﹐相減後不能確定其值是0﹐所以要加C

👍 0 👎 0

Pak Woon

2006-10-20 7:21 pm

∫3 dx - 3*∫dx

=∫3 dx - 3*∫1 dx

=3x+C1-3(x-C2) (where C1, C2 are arbitary constant)

=C1-3*C2

=C (since it is only an arbitary constant, we could change the variable)

參考: A maths textbook

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haha

2006-10-20 7:01 pm

∫3 dx - 3*∫dx

=∫3 dx - 3*∫1 dx

=3x+C1-3x-C2

=C1-C2

=C

應該加C

又

∫3 dx - 3*∫dx

=3*∫1 dx - 3*∫1 dx

=3(∫1 dx - ∫1 dx)

=3∫(1- 1) dx

=3C1

=C

參考: me

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weiling lim

2006-10-20 12:09 pm

係要plus C架
因為如果work backwards
for eg C = 2,
d/dx 2 都係得返個零
所以唔可以排除非零既answer :D

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