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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Andiio on June 26, 2011, 03:54:26 pm

Title: Integration Variable
Post by: Andiio on June 26, 2011, 03:54:26 pm: 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!
Title: Re: Integration Variable
Post by: pi on June 26, 2011, 04:01:56 pm: Yep, I do. It obeys fraction laws.

Can't do it for $\frac{d^2y}{dx^2}$ though
Title: Re: Integration Variable
Post by: Andiio on June 26, 2011, 04:06:31 pm: Quote from: pi on June 26, 2011, 04:01:56 pm
Yep, I do. It obeys fraction laws.

Can't do it for $\frac{d^2y}{dx^2}$ 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
Title: Re: Integration Variable
Post by: pi on June 26, 2011, 05:29:40 pm: Quote from: Andiio on June 26, 2011, 04:06:31 pm
Quote from: pi on June 26, 2011, 04:01:56 pm
Yep, I do. It obeys fraction laws.

Can't do it for $\frac{d^2y}{dx^2}$ 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 (:o) treats it as a fraction in some of their questions.

Quote from: Andiio on June 26, 2011, 04:06:31 pm
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
Title: Re: Integration Variable
Post by: taiga on June 27, 2011, 01:39:36 am: 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)