Page 2 of 2 FirstFirst 12
Results 16 to 20 of 20
Like Tree3Thanks

Math Help - How to integrate when the dx, the differential, is in the denominator?

  1. #16
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: How to integrate when the dx, the differential, is in the denominator?

    Hmm, when I do the same insertion, I get:

    {C_0 \over k} L^k = C_L(L-x)^k

    C_L = {{C_0 \over k} L^k \over (L-x)^k}

    C_L = {C_0 \over k} \left({L \over L-x}\right)^k

    Substituting k = 0.15 gives:

    C_L = {C_0 \over 0.15} \left({L \over L-x}\right)^{0.15}

    Yes, there is a difference, which suggests the original formulation is incorrect.
    Apparently, there should be a (1-k) somewhere instead of a k.

    I haven't tried to understand your process yet, but is it possible it should have been:

    (1-k)C_L dx=(L-x) dC_L
    Last edited by ILikeSerena; January 16th 2013 at 11:28 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Newbie
    Joined
    Jan 2013
    From
    Israel
    Posts
    9

    Re: How to integrate when the dx, the differential, is in the denominator?

    It makes sense, on left is the quantity of the impurity that is left in the zone after dx has solidified, (1-x), and it is equal to the increase, dCL, in the concentration in the shortening zone (L-x). then the result is as it should be.
    But let me ask a mathematical question:
    Why don't i have dx on the right side also, on the side of (L-x)?
    L-x is shortening with the amount dx also.
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: How to integrate when the dx, the differential, is in the denominator?

    Hmm, I still don't understand your process.

    But okay, let's take a look at your shortening zone.

    Then apparently at some point in time the zone is (L-x).
    Then it is shortened by an infinitesimal amount dx, so it becomes (L-x-dx).
    Since dx is very small, it can be neglected relative to (L-x).
    So it is the same as just (L-x), especially if we let dx approach zero.
    Last edited by ILikeSerena; January 17th 2013 at 01:25 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: How to integrate when the dx, the differential, is in the denominator?

    I don't get it.
    How should L be shortening?
    Isn't L the fixed width of the furnace?

    Oh wait, are we looking at the last part of the process only? When the last part of the bar is leaving the furnace?
    Last edited by ILikeSerena; January 17th 2013 at 01:26 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Newbie
    Joined
    Jan 2013
    From
    Israel
    Posts
    9

    Re: How to integrate when the dx, the differential, is in the denominator?

    yes, but i think i am getting the answer to my question, thanks to you all
    Karol
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. How to integrate this partial differential equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: December 28th 2012, 04:56 PM
  2. Replies: 4
    Last Post: November 15th 2011, 05:48 AM
  3. Integrate second order differential equation
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: August 31st 2010, 08:24 PM
  4. Can't integrate this differential equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 4th 2010, 10:13 AM
  5. help find the denominator
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 6th 2009, 11:09 AM

Search Tags


/mathhelpforum @mathhelpforum