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Method of disk (in respect to y)

  1. Mar 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Revolve the region under the curve y =√x on the interval [0, 4] about the x-axis and
    find the volume of the resulting solid of revolution.

    YET, NOW, I want to do in respect to y

    2. Relevant equations
    integral formula

    3. The attempt at a solution

    I did dx and I got 8pi which is corrected.

    So I decided to do it with dy.

    I looked at the graph and I saw the height would be the same (well because of the problem's nature). so a and b will stay the same

    integral of pi*r^2
    we know r is y^2 (since y^2 = x)
    integral of pi * (y^2)^2 from 1 to 4

    but I did not get 8pi

  2. jcsd
  3. Mar 6, 2010 #2


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    Homework Helper

    The integral you evaluated, gives the volume when the curve is rotated about the y-axis, not the x-axis.
  4. Mar 7, 2010 #3
    The original function was y = sqrt of x
    so inverse it, we got x = y^2

    you were right about the fact. i think the point of a and b should be 0 to 2, since y^2 = x, so (2^2) = 4

    integral of pi * (y^2)^2 from 0 to 2
    but i got 16/5 instead
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