How can I deal with such an integral？

[rtransformation]

Homework Statement

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?

Homework 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.

The Attempt at a Solution

 

[MidgetDwarf]

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

 

[rtransformation]

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

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?

 

[serp777]

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?

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.

 

[SteamKing]

Homework Statement

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?

Homework 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.

The Attempt at a Solution

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 = e^x, 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.

 

[rtransformation]

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 = e^x, 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.

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 ...

 

[SteamKing]

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 ...

Not that I'm aware of.

 

[Mark44]

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?

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.

 

[rtransformation]

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.

Thank you