Integration Variable

[Andiio]

Are we technically allowed to treat the integration variable as a 'fraction'?

E.g. when using substitution to simplify the integrand, say we have y = √16-x^2,

Let x = 4sin(theta), so dx/d(theta) = 4cos(theta)

are we allowed to then equate dx = 4cos(theta)d(theta)?

Thanks!

[pi]

Yep, I do. It obeys fraction laws.

Can't do it for though

[Andiio]

Yep, I do. It obeys fraction laws.

Can't do it for though

Are you sure? :O I asked my teacher and he said in some cases it's technically 'illegal', so I haven't been doing it with linear substitution.. but with trig substitution it does get quite hard not to treat it as a fraction. :\

Could you please elaborate more on d^2y/dx^2?

Moderator action: removed real name, sorry for the inconvenience

[pi]

Yep, I do. It obeys fraction laws.

Can't do it for though

Are you sure? :O I asked my teacher and he said in some cases it's technically 'illegal', so I haven't been doing it with linear substitution.. but with trig substitution it does get quite hard not to treat it as a fraction. :\

It's not illegal at all. In fact, even MathsQuest () treats it as a fraction in some of their questions.

Could you please elaborate more on d^2y/dx^2?

Sorry, not sure on the exact reason, I just know that it definitely doesn't obey fraction laws.

Moderator action: removed real name, sorry for the inconvenience

[taiga]

I do this for separable differential equations all the time (the ones where you need to move all the x's and y's to one side).

Pretty sure you should be okay (Y)