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Error in Thomas' Calculus 13th edition?

  1. Aug 12, 2016 #1
    1. The problem statement, all variables and given/known data
    Section 11-2, Page 651, Example 3

    2. Relevant equations
    y = sin^3t and dy = 3cos^2t sint dt. Shouldn't there be a Minus Sign there?

    3. The attempt at a solution
    Answer is correct. But isn't there a missing Minus Sign?
     
  2. jcsd
  3. Aug 12, 2016 #2
    What makes you think that? Shouldn't it be ##3sin^2tcostdt##?
     
  4. Aug 12, 2016 #3

    Stephen Tashi

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    Shouldn't that be "##3 \sin^2{t} \cos{t}\ dt##" ?
     
  5. Aug 12, 2016 #4
    The book has x-=cos^3 t and dx = 3 cos^2 t sin t dt That's where the minus sign appears to be missing.
     
  6. Aug 12, 2016 #5

    Stephen Tashi

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    I don't understand the notation "x-=". You didn't say where the minus sign is missing.
     
  7. Aug 13, 2016 #6

    epenguin

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    He doesn't fill in the missing steps? No they don't always, you are expected to do it yourself.

    Best not to try and do this one in your head alone. Write it out and if you still have a problem ask again giving your work.

    You're sure you copied the formulae exactly to us? As it stands, it looks like he has used some trigonometrical identitiy/ies which makes it not immediately obvious to most people.
     
  8. Aug 13, 2016 #7

    SammyS

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    Hello Daniel McKinley. Welcome to PF !

    It helps greatly to give us the entire problem (in this case an Example) as it was given in the textbook.

    Here is a screen shot of what I could find for that example:
    upload_2016-8-13_12-13-57.png

    The author has done the problem correctly. As @epenguin has suggested, the author has skipped some steps.

    Indeed, ##\ dx = -3\cos^2 t \sin t \,dt\ ## with a negative sign.

    If you consider the limits of integration, the negative sign has the effect of switching the limits of integration, giving the integral you see above.
     
  9. Aug 13, 2016 #8
    Thank you SammyS!
     
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