# How can I deal with such an integral？

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1. Dec 23, 2015

### rtransformation

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. Dec 23, 2015

### MidgetDwarf

I think you are referring to the fundamental theorem of calculus?

3. Dec 23, 2015

### rtransformation

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?

4. Dec 23, 2015

### serp777

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.

5. Dec 23, 2015

### SteamKing

Staff Emeritus
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.

BTW, you integrate functions, you don't 'integral' them.

6. Dec 23, 2015

### rtransformation

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 ....

7. Dec 23, 2015

### SteamKing

Staff Emeritus
Not that I'm aware of.

8. Dec 23, 2015

### 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.

9. Dec 23, 2015

Thank you