# Thread: Integration problem: is my textbook wrong?

1. ## 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?

2. 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?
$\displaystyle \int (10x-3)(5x^2 - 3x + 17)^{1/7}dx$
Call,
$\displaystyle u=5x^2-3x+17$ then,
$\displaystyle du/dx=10x-3$
Thus,
$\displaystyle \int u^{1/7} \frac{du}{dx} dx$=
$\displaystyle \int u^{1/7} du$
Thus, exponents rule,
$\displaystyle \frac{u^{1/7+1}}{1+1/7}+C=\frac{7}{8}u^{8/7}$
Thus,
$\displaystyle \frac{7}{8}(5x^2-3x+17)^{8/7}+C$

3. ## 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).

4. 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?

5. ## 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