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Homework Help: How can I deal with such an integral?

  1. Dec 23, 2015 #1
    1. The problem statement, all variables and given/known data
    How can I deal with such an integral: the integrand include another variable which has some relationship with the variable of integration, but i do not know the exact relationship. Can I just see the "another variable" mentioned above as a invariant and put it outside from the integral symbol?
    I think I cannot do so, but how can I handle such a question?

    2. Relevant equations
    For example, dy=z*dx, where some unknown relationship with the x, i think i can't integral it m the two sides and just put the z outside from the integral symbol.

    3. The attempt at a solution
  2. jcsd
  3. Dec 23, 2015 #2
    I think you are referring to the fundamental theorem of calculus?
  4. Dec 23, 2015 #3
    I mean if i want to integral the dy=z*dx or something like this with an unknown z which may have some relation with the x, how can i do? Is there some area of mathematics concerning this kind of questions?
  5. Dec 23, 2015 #4
    If you're only dealing with the relationship between x and y as specified by dy and dx, then Z is just a constant i would image. Its like when you integrate and you get the + c constant added, but that C variable isn't one of the relationships in the equations.

    so if you integrate z*dx then basically its just the integral of a constant with respect to x. And yeah you can just pull it out like a constant.
  6. Dec 23, 2015 #5


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    This is pretty vague.

    If z does not have a dependence on the variable of integration x, it can be treated as a constant.
    If z does have some unknown dependence on the variable of integration, it cannot be treated as a constant, but you cannot integrate until the correct relationship between z and x is established.

    For example, if z = ex, then ∫ z dx would give one result, but if z = sin (x), then ∫ z dx would give a completely different result.

    That's just math. :frown:

    BTW, you integrate functions, you don't 'integral' them.
  7. Dec 23, 2015 #6
    haha, Thank you, i just can't remember the correct word, thank you again
    isn't there exist a method to handle the uncertain z? that baffles me ....
  8. Dec 23, 2015 #7


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    Not that I'm aware of.
  9. Dec 23, 2015 #8


    Staff: Mentor

    I agree with SteamKing. In the integral ##\int z~ dx##, where z is some function of x, it's not possible to find an antiderivative without knowing how z is related to x.
  10. Dec 23, 2015 #9
    Thank you
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