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Homework Help: Finding out the amount of glass through integration

  1. May 11, 2010 #1
    1. The problem statement, all variables and given/known data
    A glass vase has the shape of the solid obtained by rotating about the y–axis the area in
    the first quadrant lying over the x–interval [0,a] and under the graph of y = [tex]\sqrt{x}[/tex]
    Determine how much glass is contained in the vase.

    2. Relevant equations
    y = [tex]\sqrt{x}[/tex]

    3. The attempt at a solution
    I know the integration to find the area under the graph would be
    F = 2/3x^(3/2)

    Area = [tex]\int2/3x^(3/2)[/tex] from 0 to a
    and you would need to times the total area by 2 to get the full "vase"

    Thanks alot!
  2. jcsd
  3. May 11, 2010 #2


    Staff: Mentor

    This is not a precalculus problem. Post calculus problems in the Calculus & Beyond section.
    This is the antiderivative of x1/2. To get the area, you need a definite integral.

    However, this problem is not asking for the "area" of glass. It's asking for the volume of glass.
    This makes no physical sense. You are attempting to take the antiderivative of a function that is the antiderivative of x1/2.

    This problem involves calculating the volume of revolution. There are two ways to calculate a volume of revolutions: breaking the solid up into disks or breaking the solid up into thin cylindrical shells. Your textbook should have examples of each of these techniques.
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