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Volume of revolution

  1. Apr 15, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the volume generated by rotating the area bounded by y=2+x and y=x^2 about the y-axis.

    2. Relevant equations
    Volume of revolution.

    3. The attempt at a solution
    shell method
    integral (0 to 2) of x(2+x-x^2) dx

    I think this can be solved by eliminating the left part and only count the volume of the left side, because the left part of the solid result is covered by the right part. It's a problem in my school because our teacher is debating whether the left part is counted or not.

    i'm sorry i can't write in equotion.. i'm newbie
  2. jcsd
  3. Apr 15, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    IF the problem really says "rotate around the y-axis, then you are right: the solid is generated is by the region between y= x+ 2 and y= x2 for x> 0. The problem would make more sense and be more interesting if it were rotated around the x-axis.
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