Expert: Paul Klarreich - 10/19/2006

Question
Sorry, I don't know what happened but I hope you could read it this time, and thanks a lot for your help!
(S is the intergration notation.)

Integration: S3dx - 3*Sdx

I don't know if I should +C...
The answer seems to be 0 as S3dx = 3*Sdx
but I don't think it make sense if I don't +C...  

Answer
Questioner:  Priere
Category:  Calculus
Private:  no
 
Subject:  RE: Integration: Special case...
Question:  Sorry, I don't know what happened but I hope you could read it this time, and thanks a lot for your help!
(S is the integration notation.)

Integration: S3dx - 3*Sdx

I don't know if I should +C...
The answer seems to be 0 as S3dx = 3*Sdx
but I don't think it make sense if I don't +C...
.....................................................

Hi, Priere,

Is this what you mean to write?  [BE SURE TO VIEW THIS IN A FIXED FONT.]


{          {
| 3 dx - 3 | dx = ...
}          }

In that case, you are correct to state that the answer is a constant.  You are basically doing the following:

{        {
| 3 dx - | 3 dx =
}        }


{        
| [ 3 - 3 ] dx =
}         

{        
| 0 dx =
}        

Now to answer this, you really have to focus on the question.  It says, "What function gives a derivative of zero?"

Once you realize that's the question, the answer becomes obvious.  A CONSTANT function gives zero as its derivative.