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Math Help - Integration problem: is my textbook wrong?

  1. #1
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    Integration problem: is my textbook wrong?

    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

    (7/8) [(5x^2 - 3x + 17)^(8/7)] + C.

    The author's is

    (7/8) [(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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  2. #2
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    Quote Originally Posted by lingyai
    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

    (7/8) [(5x^2 - 3x + 17)^(8/7)] + C.

    The author's is

    (7/8) [(5x^2 - 3x - 17)^(8/7)] + C.

    Note that we differ only over whether one should add or subtract 17.

    Who's right?
    <br />
\int (10x-3)(5x^2 - 3x + 17)^{1/7}dx
    Call,
    u=5x^2-3x+17 then,
    du/dx=10x-3
    Thus,
    \int u^{1/7} \frac{du}{dx} dx=
    \int u^{1/7} du
    Thus, exponents rule,
    \frac{u^{1/7+1}}{1+1/7}+C=\frac{7}{8}u^{8/7}
    Thus,
    \frac{7}{8}(5x^2-3x+17)^{8/7}+C

    YOUR SOLUTION IS CORRECT!
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  3. #3
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    Thanks very much

    Very reassuring, thanks a lot. This text is supposed to be a self-contained, self-teaching guide. Overall it is great, but these things drive me crazy . It's the 10th one I've found (or confirmed, thanks to people like you).
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  4. #4
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    Quote Originally Posted by lingyai
    Very reassuring, thanks a lot. This text is supposed to be a self-contained, self-teaching guide. Overall it is great, but these things drive me crazy . It's the 10th one I've found (or confirmed, thanks to people like you).
    Just curious what edition is your book?
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  5. #5
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    Re errors in Barbara Lee Bleau's "Forgotten Calculus"

    The edition I've been discussing is the 3rd edition, 2002, ISBN 0-7641-1998-2.

    I'm almost through with the book and will be posting a list of errata with the Amazon reviiew I'll write. If you'd like me to send you the list directly let me know.

    I should say that the typos aside -- and that's a big aside -- it is still an excellent text for the likes of me (fairly average math ability) and students of lower ability. She certainly has a gift for clear explanation. I've done every exercise in 26 of the 28 units so far, some of them more than once. At the end of the day, I do feel I've got a grasp of the material which I wouldn't have imagined when I started.

    In turn, I have a question for you -- do you know of an inexpensive fairly accesible text for multivariate calculus? Bleau saves this for the final (brief) chapter and I think I'll need to go into more depth in order to handle the stochastic modelling which my graduate program (which starts in 4 months) will involve.

    Anyway, thanks again for your help,

    Ken
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