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Solid Volume with integration

  1. Jan 28, 2008 #1
    1. The problem statement, all variables and given/known data

    The base is the region enclosed by y=x^2 and y=3. The cross sections perpendicular to the y-axis are rectangles of height y^3.

    Use the information to solve for the volume of the solid.

    2. Relevant equations



    3. The attempt at a solution

    I tried to find the base and height of the cross sections in terms of y, since the parabola is 2y^1/2 across for any height that is the base of the rectangular cross section is 2y^1/2 and the height will be y^3. This means the area of the cross section is the product of (2y^1/2)*y^3 =2*y^(7/2) then this integrated from 0 to 3 should give me the volume? I ended up getting 48/9 * 3^1/2 or 4/9 * 3^(9/2) could anyone verify this?
     
  2. jcsd
  3. Jan 29, 2008 #2
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