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Find the volume of the solid

  1. Mar 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid generated by revolving the region bounded by the parabola y=x^2 and the line y=1 about the line y=1


    2. Relevant equations
    V= integral of pi*r^2 from a to b with respect to variable "x"


    3. The attempt at a solution
    pi(integral of 1-(x^2-1)^2 from 0 to 1 dx)
    but The answer is 15pi/16
     
  2. jcsd
  3. Mar 23, 2014 #2

    Dick

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    Why do you think the 'r^2' part in your volume equation is 1-(x^2-1)^2 and why do you think the limits to the integration are 0 to 1?
     
  4. Mar 23, 2014 #3
    r^2
    1 represents outer radius (the larger radius)
    x^2-1 represents the inner radius (smaller radius)

    limits to integration
    the radius of the sphere is on the region x= 0 to 1
     
  5. Mar 23, 2014 #4
    r^2
    1 represents outer radius (the larger radius)
    x^2-1 represents the inner radius (smaller radius)

    limits to integration
    the radius of the sphere is on the region x= 0 to 1
     
  6. Mar 23, 2014 #5

    Dick

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    That's confusing me. The formula you gave was actually for the method of disks, which is what I would use here. If you are rotating the region between y=x^2 and y=1 around y=1, then the inner radius is 0, isn't it? And I don't see why you are putting one of the limits to 0. y=x^2 and y=1 cross at x=1 and x=(-1), yes?
     
  7. Mar 23, 2014 #6
    Yes. Yes. I came up with my original answer because at the outer region 1= radius so we have one and at the inner region 0 = radius as (1^2-1)^2=0

    I have only studied the washer method.
     
  8. Mar 23, 2014 #7
    Yes. Yes. I came up with my original answer because at the outer region 1= radius so we have one and at the inner region 0 = radius as (1^2-1)^2=0

    I have only studied the washer method.
     
  9. Mar 23, 2014 #8

    Dick

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    The disk method is the same as the washer method with an inner radius of 0. Isn't the outer radius ALWAYS 1-x^2? And the inner radius 0?
     
  10. Mar 23, 2014 #9
    I correct myself, I have studied disc method. Yes. yes.
     
  11. Mar 23, 2014 #10
    I correct myself, I have studied disc method. Yes. yes.
     
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