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lingyai
science forum beginner
Joined: 14 Apr 2006
Posts: 21
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 Posted: Fri May 19, 2006 8:26 pm Post subject:
Integration problem: who's wrong, the textbook or me?
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I think I might have found a typo in my calculus text, "Forgotten Calculus". It would not be the first. Anyway, if it is I and not the author who is wrong, then I'm missing something fundamental, and would appreciate guidance.
The problem asks to find the integral of
(10x - 3) [(5x^2 - 3x + 17)^(1/7)] dx
via substitution.
My solution is
(7/ [(5x^2 - 3x + 17)^(8/7)] + C.
The author's is
(7/ [(5x^2 - 3x - 17)^(8/7)] + C.
Note that we differ only over whether one should add or subtract 17.
Who's right? |
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Brian M. Scott
science forum Guru
Joined: 10 May 2005
Posts: 332
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| Posted: Fri May 19, 2006 8:34 pm Post subject:
Re: Integration problem: who's wrong, the textbook or me?
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On Fri, 19 May 2006 16:26:06 EDT, lingyai
<ken_kasriel@yahoo.com> wrote in
<news:27784590.1148070396316.JavaMail.jakarta@nitrogen.mathforum.org>
in alt.math.undergrad:
| Quote: | I think I might have found a typo in my calculus text,
"Forgotten Calculus". It would not be the first. Anyway,
if it is I and not the author who is wrong, then I'm
missing something fundamental, and would appreciate
guidance.
The problem asks to find the integral of
(10x - 3) [(5x^2 - 3x + 17)^(1/7)] dx
via substitution.
My solution is
(7/ [(5x^2 - 3x + 17)^(8/7)] + C.
The author's is
(7/ [(5x^2 - 3x - 17)^(8/7)] + C.
Note that we differ only over whether one should add or
subtract 17.
Who's right?
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You are; it's a typo in the text.
Brian |
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Badger
science forum beginner
Joined: 07 May 2006
Posts: 38
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| Posted: Fri May 19, 2006 9:06 pm Post subject:
Re: Integration problem: who's wrong, the textbook or me?
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On Fri, 19 May 2006 16:26:06 EDT, lingyai <ken_kasriel@yahoo.com>
wrote:
| Quote: | I think I might have found a typo in my calculus text, "Forgotten Calculus". It would not be the first. Anyway, if it is I and not the author who is wrong, then I'm missing something fundamental, and would appreciate guidance.
The problem asks to find the integral of
(10x - 3) [(5x^2 - 3x + 17)^(1/7)] dx
via substitution.
My solution is
(7/ [(5x^2 - 3x + 17)^(8/7)] + C.
The author's is
(7/ [(5x^2 - 3x - 17)^(8/7)] + C.
Note that we differ only over whether one should add or subtract 17.
Who's right?
|
You are correct. For future reference, here's a site where you can
check your integrals:
<http://integrals.wolfram.com/> |
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lingyai
science forum beginner
Joined: 14 Apr 2006
Posts: 21
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| Posted: Fri May 19, 2006 9:35 pm Post subject:
Re: who's wrong, the textbook or me?-- THANKS BOTH OF YOU!
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Very reassuring. I've only been doing integration since yesterday and thought I was losing my marbles... |
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W H G
science forum beginner
Joined: 03 Aug 2005
Posts: 11
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| Posted: Fri May 19, 2006 10:53 pm Post subject:
Re: Integration problem: who's wrong, the textbook or me?
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"lingyai" <ken_kasriel@yahoo.com> wrote in message
news:27784590.1148070396316.JavaMail.jakarta@nitrogen.mathforum.org...
| Quote: | I think I might have found a typo in my calculus text, "Forgotten
Calculus". It would not be the first. Anyway, if it is I and not the author
who is wrong, then I'm missing something fundamental, and would appreciate
guidance.
The problem asks to find the integral of
(10x - 3) [(5x^2 - 3x + 17)^(1/7)] dx
via substitution.
My solution is
(7/ [(5x^2 - 3x + 17)^(8/7)] + C.
The author's is
(7/ [(5x^2 - 3x - 17)^(8/7)] + C.
Note that we differ only over whether one should add or subtract 17.
Who's right?
|
Checking your work - against the problem not the text - is
always a good idea. In this case, just take the derivative and
what you integrated had better be what you get. Without doing
the detail it is apparent that d/dx [(5x^2 - 3x + 17)^(8/7)]
will have +17 in the parans not -17.
--- W H G |
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lingyai
science forum beginner
Joined: 14 Apr 2006
Posts: 21
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| Posted: Sun May 21, 2006 2:06 pm Post subject:
Re: Integration problem: who's wrong, the textbook or me?
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Thanks. I had checked my work several times before posting this question. But having only started the section on integration that day, and using a book which has received many good reviews (see Amazon, for example), I assumed I must have been wrong. |
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