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Identity

Member

Registered: 2007-04-18

Posts: 934

Constant of integration with a plus/minus?

I'm doing a physics question and I've come to a point where I have

Continuing on,

Suppose

is the antidervative of

and C is a constant, then which of the following is true?

I need to know because the positive solution satisfies one condition and the negative solution must satisfy another condition. Basically, I'll end up with simultaneous equations and I need to know whether or not C has the same sign in both.

Last edited by Identity (2011-02-20 19:44:17)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Constant of integration with a plus/minus?

hi Identity,

Firstly, did you mean

as you had a 'square' on the line above.

Now to your question.

A constant of integration is just a number that has to be found by using other information that is known to you about the problem (called boundary condition(s)  ).

It doesn't matter whether you use a plus sign or a minus because the boundary conditions will sort that out for you.

A week or so back, bobbym and I each helped someone with an integration problem and, at first, we thought one of us must be wrong, because we had a different sign at a point in our answers.  But, at the end the constant of integration took care of the difference for us.  Where I made C a positive amount, bobbym made his 'C' the same but negative amount.  So our final answers were the same.

All you need to do is decide which sign you will use for C, and stick to it consistently, throughout the solution.

Bob

ps.  Post the actual f(y) if you want further help.

Last edited by Bob (2011-02-20 21:09:31)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Constant of integration with a plus/minus?

Thanks for the reply bob, I'm sorry I couldn't make it very clear because it is an assignment question

However, I think my problem is somewhat similar to the well-known Brachistochrone problem, which models the fastest way to 'slide' down a slope.

It has the equation 

Solving for

,

Suppose the antiderivative of

is

Then do we have

or

?

Take the boundary conditions to be

,

With the Brachistochrone problem it's easier - the ending height is always less than the starting height, so you know that

must be negative, leaving you with one equation, 2 unknowns, and 2 boundary conditions. But what if you couldn't assume that? My problem is more complicated because intuitively I know that

changes from negative to positive. So I think I would have

for

for

Last edited by Identity (2011-02-22 15:45:24)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Constant of integration with a plus/minus?

hi Identity,

I have been assuming that 'C' was the constant of integration. 

But it isn't in this:

Later you do have another 'C', where it is the constant of integration, and not necessarily the same 'C'.

Whatever,  I think you should use

in all cases.  If 'C' should have been negative, it will come out as this, when you substitute values.

Bob

Last edited by Bob (2011-02-23 01:40:07)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Constant of integration with a plus/minus?

Gah! Two mistakes for me in two posts

Anyway thanks for the advice bob, I'll try and work through it with that