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Variable constant?

  1. Apr 14, 2007 #1
    1. The problem statement, all variables and given/known data
    Does the term variable constant make sense?
    There could also be an integration variable.

    i.e in a function W(x) = int(e^(xy)) where y is the integration variable. So is x in this situation the constant variable? Or is the word constant unnecessary.

    But in W(x)=x, x would be just be the variable.
     
  2. jcsd
  3. Apr 14, 2007 #2

    HallsofIvy

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    No, the term "constant variable" makes no sense. Nor does it apply to the situation you cite. x could be a constant or it could be a variable exy is being integrated with respect to b. I.e. at each value of x.
     
  4. Apr 14, 2007 #3
    you mean wrt y?

    So W(x)=int(e^xy)dy but x is still a variable. Just like in W(x)=x. Do you think functions like W(x)=int(e^xy)dy is strange? Where or how does it appear usually?
     
  5. Apr 14, 2007 #4

    cepheid

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    [tex] W(x) = \int_{y_1}^{y_2} f(x,y)\,dy [/tex]

    doesn't seem that strange to me. The integrand is a function of two variables, but when you integrate over y, the y-dependence is eliminated, and what remains is a function of x only. Integration wrt y just gives you a number (in this case, a different number FOR EACH value of x). So what remains is a function of x.
     
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