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#1 2007-07-28 09:56:41

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Understanding Definite Integrals

Which phrase best describes a definite integral:

1.)  A net accumulated change

2.)  A net accumulation of amounts

3.)  A net accumulation of changing amounts

Any discussion would be appreciated.  Thank you.
(I got the idea for this question from listening to some of the first videos available from the MidnightTutor.COM folks.)


igloo myrtilles fourmis

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#2 2007-08-01 15:56:16

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Understanding Definite Integrals

A might be better.

Because you can integrate sth from 1 to 2 whereas you can integrate it from 2 to 1, either way.

Change is more neutral than accumulation, which implies a possitive amount.


X'(y-Xβ)=0

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#3 2007-08-01 19:18:14

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Understanding Definite Integrals

Change is more neutral than accumulation, which implies a possitive amount.

I disagree, I don't see accumulation implying positive.  For example, one can accumulate debt, which is in effect negative money.

2 would be my answer.  Because when you are taking the definite integral of a function under certain bounds, what you are computing is the area under that function.  As such, it is a accumulation of amounts.  Accumulation of change sounds to me like something that would be using derivatives (change in slope).


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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