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Volume by integration

  1. Mar 29, 2016 #1
    1. The problem statement, all variables and given/known data
    I have the attached problem ,and Show my answer and solution,

    My answer is 3.14*(15 -8ln4)
    While book answer 3.14(15+8ln)
    IMG_2214.jpg
    Can any one point to the mistake I made???
     
  2. jcsd
  3. Mar 29, 2016 #2

    Charles Link

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    Homework Helper

    Your calculation looks correct to me. I don't see any obvious errors.
     
  4. Mar 29, 2016 #3
    Your work also looks good to me.
    The one thing I noticed is the answer from the book would be right if you take the negative away from the 1.

    I'm guessing the book has a typo.
     
  5. Mar 30, 2016 #4

    Mark44

    Staff: Mentor

    If this is actually the book's answer, it makes no sense without something following ln.
     
  6. Mar 30, 2016 #5
    Thanks
    Absolutely right, but draw the function, you will see that volume is almost as his answer(using geometry not integration),and that why I am confused.
     
  7. Mar 30, 2016 #6

    Ray Vickson

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    Science Advisor
    Homework Helper

    If you think that the book's answer ##\pi (15+8 \ln(4))## is close to the correct answer you are very much mistaken. The correct answer is yours, except that the approximation ##\pi = 3.14## is way too crude---just leave it as symbolic ##\pi## until it comes time to evaluate the final answer numerically. Look at the following:
    [tex]\begin{array}{rccc}
    \pi (15 - 8 \ln\,4 )& \doteq & 12.28251236 & \doteq & 12.3 \\
    \pi (15 + 8 \ln\,4 ) & \doteq & 81.96526726 & \doteq & 82.0 \\
    \pi 15 & \doteq & 47.12388981 & \doteq & 47.1
    \end{array}

    [/tex]
     
  8. Mar 31, 2016 #7
    you
    You are right his answer is not logical,

    Thanks
     
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