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lingyai
science forum beginner
Joined: 14 Apr 2006
Posts: 21
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 Posted: Wed May 24, 2006 8:37 am Post subject:
Need feedback on a basic integration concept
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In my calculus text I have found something which is either a typo or a basic concept which I'm missing. I'd be grateful for opinions.
(By the way, this is not the first such question I've posted. It's not being pedantic; rather, I just want to ensure I'm not learning the wrong thing, or failing to learn the right thing. Because it is a high-selling, well-reviewed text ("Forgotten Calculus", by Barbara Lee Bleau)my first assumption is that I am wrong).
The relevant part of the question asks to find the integral of (1-x)^(2) dx.
But in the solution, the function to integrate is restated at the outset as (1- x^(2)) dx.
Based on my (admittedly novice) understanding of integration, these functions, and hence their integrals, are not the same.
For the integral of (1-x)^(2), I get
integral (1 - 2x + x^(2))
= x - x^2 + ((x^3)/3)
while for the integral of (1 - x^(2)) I get
x - (x^3)/3
Again -- am I right, or is there some reason that for the purposes of integration,
(1-x)^(2) = (1- x^(2))? |
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Patrick
science forum addict
Joined: 01 Feb 2006
Posts: 55
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| Posted: Wed May 24, 2006 9:38 am Post subject:
Re: Need feedback on a basic integration concept
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lingyai wrote:
| Quote: | In my calculus text I have found something which is either a typo or a basic concept which I'm missing. I'd be grateful for opinions.
(By the way, this is not the first such question I've posted. It's not being pedantic; rather, I just want to ensure I'm not learning the wrong thing, or failing to learn the right thing. Because it is a high-selling, well-reviewed text ("Forgotten Calculus", by Barbara Lee Bleau)my first assumption is that I am wrong).
The relevant part of the question asks to find the integral of (1-x)^(2) dx.
But in the solution, the function to integrate is restated at the outset as (1- x^(2)) dx.
Based on my (admittedly novice) understanding of integration, these functions, and hence their integrals, are not the same.
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That's correct.
| Quote: | For the integral of (1-x)^(2), I get
integral (1 - 2x + x^(2))
= x - x^2 + ((x^3)/3)
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Right, and the +C. No big deal.
| Quote: | while for the integral of (1 - x^(2)) I get
x - (x^3)/3
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That's correct, plus the +C :)
| Quote: | Again -- am I right, or is there some reason that for the purposes of integration,
(1-x)^(2) = (1- x^(2))?
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Looks like a typo.
I haven't used that particular book but I have noticed
that books of that type tend to have lots of typos. |
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William Elliot
science forum Guru
Joined: 24 Mar 2005
Posts: 1906
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| Posted: Wed May 24, 2006 11:14 am Post subject:
Re: Need feedback on a basic integration concept
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On Wed, 24 May 2006, lingyai wrote:
| Quote: | In my calculus text I have found something which is either a typo or a
basic concept which I'm missing. I'd be grateful for opinions.
The relevant part of the question asks to find the integral of (1-x)^(2) dx.
But in the solution, the function to integrate is restated at the outset
as (1- x^(2)) dx.
Modern publishing bent upon money productivity instead of accurate texts, |
is frought with mistakes, even some false statements and fraud. Like new
drugs, it's cheaper, ie makes the CEO bigger monies, to let the reader,
the patient, to find, to suffer their mistakes.
| Quote: | For the integral of (1-x)^(2), I get
integral (1 - 2x + x^(2))
= x - x^2 + ((x^3)/3)
while for the integral of (1 - x^(2)) I get
x - (x^3)/3
Again -- am I right,
|
Yes.
| Quote: | or is there some reason that for the purposes of integration,
No. |
| Quote: | (1-x)^(2) = (1- x^(2))?
Of course not almost everywhere. |
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David C. Ullrich
science forum Guru
Joined: 28 Apr 2005
Posts: 2250
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| Posted: Wed May 24, 2006 11:16 am Post subject:
Re: Need feedback on a basic integration concept
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On Wed, 24 May 2006 04:37:44 EDT, lingyai <ken_kasriel@yahoo.com>
wrote:
| Quote: | In my calculus text I have found something which is either a typo or a basic concept which I'm missing. I'd be grateful for opinions.
(By the way, this is not the first such question I've posted. It's not being pedantic; rather, I just want to ensure I'm not learning the wrong thing, or failing to learn the right thing. Because it is a high-selling, well-reviewed text ("Forgotten Calculus", by Barbara Lee Bleau)my first assumption is that I am wrong).
The relevant part of the question asks to find the integral of (1-x)^(2) dx.
But in the solution, the function to integrate is restated at the outset as (1- x^(2)) dx.
Based on my (admittedly novice) understanding of integration, these functions, and hence their integrals, are not the same.
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Well of course they're not the same. You should have _some_ confidence
here - when you see something that might be a typo or might be
something subtle you should ask someone about that, but
when you see something that seems to say that (1-x)^2 = 1-x^2
you should just realize it's a typo.
| Quote: | For the integral of (1-x)^(2), I get
integral (1 - 2x + x^(2))
= x - x^2 + ((x^3)/3)
while for the integral of (1 - x^(2)) I get
x - (x^3)/3
Again -- am I right, or is there some reason that for the purposes of integration,
(1-x)^(2) = (1- x^(2))?
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************************
David C. Ullrich |
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G.E. Ivey
science forum Guru
Joined: 29 Apr 2005
Posts: 308
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| Posted: Thu May 25, 2006 11:20 pm Post subject:
Re: Need feedback on a basic integration concept
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| Quote: | On Wed, 24 May 2006, lingyai wrote:
In my calculus text I have found something which is
either a typo or a
basic concept which I'm missing. I'd be grateful
for opinions.
The relevant part of the question asks to find the
integral of (1-x)^(2) dx.
But in the solution, the function to integrate is
restated at the outset
as (1- x^(2)) dx.
Modern publishing bent upon money productivity
instead of accurate texts,
is frought with mistakes, even some false statements
|
Sometimes even replies on Math Forum are frAught with mistakes! I wouldn't go so far as to impute "fraud" to either group.
| Quote: | and fraud. Like new
drugs, it's cheaper, ie makes the CEO bigger monies,
to let the reader,
the patient, to find, to suffer their mistakes.
For the integral of (1-x)^(2), I get
integral (1 - 2x + x^(2))
= x - x^2 + ((x^3)/3)
while for the integral of (1 - x^(2)) I get
x - (x^3)/3
Again -- am I right,
Yes.
or is there some reason that for the purposes of
integration,
No.
(1-x)^(2) = (1- x^(2))?
Of course not almost everywhere. |
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