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The Disk Method

  1. Jun 24, 2009 #1
    http://www.webassign.net/www14/symImages/5/5/e52c6d3f5c64e9f5bf52f9a215f4f2.gif

    V = (pi)(r^2)


    I tried to graph this but it seemed like the graph kept going. what do i do?
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Jun 24, 2009 #2

    lanedance

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    Hi Prince

    I'm not sure I understand your question, can you elaborate?
     
  4. Jun 24, 2009 #3
    Consider the solid obtained by rotating the region bounded by the given curves about the y-axis.

    http://www.webassign.net/www14/symImages/5/5/e52c6d3f5c64e9f5bf52f9a215f4f2.gif

    Find the volume V of this solid.


    ^^

    So basically thats the question and i can't solve it.

    i started of by trying to draw in my graphing calculator, but the graph kept going.



    So i need to find the volume, can you help me?
     
    Last edited by a moderator: Apr 24, 2017
  5. Jun 24, 2009 #4

    lanedance

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    I would try graphing y = ln5x, this function is negative for x<1 and diverges to negative infinity as x heads to 0, so only plot for x>0

    Then try drawing on paper the region you want to rotate, and how it is rotated.

    Solving for the volume will involve setting up an integral. Can you write down the volume for an infintesimally thick disk?
    dV = r(y)^2.dy
    wher r(y) is the radius of the disk

    As the function is rotated around the y axis it may help to re-write your function as x in terms of y
     
    Last edited: Jun 24, 2009
  6. Jun 25, 2009 #5

    HallsofIvy

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    What do you mean by "the graph kept going"? The left boundary is x= 0, the y axis; the right boundary is the graph of y= ln(5x)= ln(5x); the lower boundary is y= 3; and the upper boundary is y= 5. Rotating around the x axis, the radius, r is x in y= ln(5x). That is, r= x= ey/5.
     
    Last edited by a moderator: Apr 24, 2017
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