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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: atar90please on August 18, 2013, 11:35:29 pm

Title: When is it necessary to add "+c" when antidifferentiating?
Post by: atar90please on August 18, 2013, 11:35:29 pm: Whilst studying antidifferentiation i noticed that +c was not always included on the end of the equation. Why is this?

MOD EDIT: Changed to a more informative title - 2/cos(c)
Title: Re: Mathematical Methods (CAS)
Post by: alondouek on August 18, 2013, 11:40:40 pm: The question may have asked for "an" antiderivative. In this case, the +c is left off because +c essentially covers every possible constant added to that antiderivative, though only one is required by the question.
Title: Re: Mathematical Methods (CAS)
Post by: atar90please on August 18, 2013, 11:43:17 pm: Ok thank you
Title: Re: When is it necessary to add "+c" when antidifferentiating?
Post by: Zealous on August 19, 2013, 03:55:29 pm: Could marks be lost if you add a +c to a question asking for "an" antiderivative? Just being pedantic =p
Title: Re: When is it necessary to add "+c" when antidifferentiating?
Post by: availn on August 19, 2013, 05:00:53 pm: Quote from: sushi. on August 19, 2013, 03:55:29 pm
Could marks be lost if you add a +c to a question asking for "an" antiderivative? Just being pedantic =p

From what I hear, no. Because even with the +c it is still "an" antiderivative. The +c just becomes optional when it goes from from "the" to "an", but everyone says to put in the +c anyways.
Title: Re: When is it necessary to add "+c" when antidifferentiating?
Post by: Phy124 on August 20, 2013, 12:41:43 am: Also just a reminder that whenever you guys find the general antiderivative of a function and add $+c$ to the end, ensure that you write something like " $, c \in \mathbb{R}$ " or "for any constant $c$ "
Title: Re: When is it necessary to add "+c" when antidifferentiating?
Post by: b^3 on August 20, 2013, 01:02:39 pm: When it says "find an anti-derivative" you don't have to add the $+c$ . Technically you shouldn't, as you'd be given a family of curves, rather than a single curve (although I guess giving many counts as giving 'an' anti-derivative).

With that being said, in cases where it does say, as above, "find an anti-derivative", VCAA accepts both.
For example, Q2 on the 2012 Methods Exam 1.
Quote
Question 2
Find an anti-derivative of $\frac{1}{(2x-1)^{3}}$ with respect to $x$ .
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2012/2012mmcas1-w.pdf

The assesors report gives this.
Quote
$-\frac{1}{4(2x-1)^{2}}+c$ When $c$ is any real number, $c$ may be omitted.
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2012/mm1_assessrep12.pdf

In other cases you'll need to add the $+c$ .

Although, for sacs and such it will depend on your teacher/who marks it.