Variable or Constant: Is the Term Variable Constant Valid?

[pivoxa15]

Homework Statement

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.

 

[HallsofIvy]

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 e^xy is being integrated with respect to b. I.e. at each value of x.

 

[pivoxa15]

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?

 

[cepheid]

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

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.