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Topic: [ap-calculus] antidifferentiation vs integration
Replies: 3   Last Post: Dec 7, 2008 8:07 AM

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BCrombie@AOL.COM

Posts: 108
Registered: 12/8/04
Re: [ap-calculus] antidifferentiation vs integration
Posted: Dec 7, 2008 8:07 AM
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To tell the brutal truth, Mark's position is equally true in mathematics and
missing that distinction misses the critical point of the Fundamental
Theorem of Calculus. Anti-derivatives are indefinite integrals. Short of that
theorem integration and anti-differentiation stand conceptually as two apparently
distinct and unrelated processes.

Bill

In a message dated 12/7/2008 7:47:00 A.M. Eastern Standard Time,
msnyder@tiac.net writes:

At 4:25 PM -0800 12/4/08, Dick Sisley wrote:
>marylou wrote:
>

>>My instinct tells me that antidifferentiation is the process we use
>>to find a function F whose derivative is given. The process of
>>integration relates more to finding the area below the given
>>function and the x-axis. Am I totalling off base?
>>

>I think you are right on base. Anti-derivatives are functions.
>Integrals are numbers.


If so, only in mathematics. Elsewhere (physics, engineering, ...), I
have never heard anyone say "antiderivative": they say "integral," as
in "the integral of x from 2 to 4" or "the integral of 2x is x^2." If
they want to get picky, they sometimes distinguish between a number
(definite integral) and a function (indefinite integral).

mark

--
mark snyder
dept of mathematics
fitchburg state college

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