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Simpson's Rule to find the volume of f(x) rotated about the x and y axis.

  1. Jun 21, 2012 #1
    1. The problem statement, all variables and given/known data
    71iut4.jpg

    Answers in the back of the book
    about x-axis= 190
    about y-axis= 828


    2. Relevant equations

    Simpson's Rule: (dx/3)* sum of(sequence of coefficients {1,4,2....2,4,1}*sequence of function values{f(0), f(1), f(2).....f(n-2),f(n-1), f(n)})

    Volume using Shells: 2π ∫ (radius)(height) dx

    Volume using Cross-Sections: π ∫ (outer radius)^2 - (inner radius)^2 dx

    3. The attempt at a solution
    2h4cjv5.jpg

    I found the area (≈) under the curve using Simpson's law, how do i rotate it without a given f(x)? The book doesn't ask for the specific method (either shells or cross-sections), but I'd like to understand how to do both. Please help.
     
  2. jcsd
  3. Jun 21, 2012 #2

    LCKurtz

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    The integral for a volume of revolution of ##f(x)## between ##a## and ##b## is$$
    V=\pi\int_a^b f^2(x)dx$$Do Simpson's rule on that, not on the area integral.
     
  4. Jun 21, 2012 #3
    we're not given f(x) though. We're only given the values of f(x)
     
  5. Jun 21, 2012 #4

    LCKurtz

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    So you can figure out the values of ##\pi f^2(x)## and do Simpsons rule just like you did for the area.
     
  6. May 26, 2013 #5
    Great question. Would someone please give more details as to combining function and s rule?
     
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