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Volume of the solid region with respect to x,y-axises, and lines x and y work shown

  1. Feb 25, 2009 #1
    Indicate the method you use to set up the integrals (do not integrate) that give the volume of the solid generated by rotating the region R around:

    The region R is bounded by the curves y=x, x= 2-y^2 and y=0

    i.) the x-axis
    ii.) the y-axis
    iii.) the line x= -2
    iv.) the line y= 1

    work shown:

    y=x ,

    x= 2- y^2
    y= sqrt(2-x)

    i.) integral of Pi*[(x)- (sqrt(2-x))] dx as x goes from 0 to 1

    ii.) integral of 2*Pi*x*[(x)-sqrt(2-x)]dx as y goes from 0 to 1

    iii.) integral of 2*Pi*(-2-x)*[(x)-(sqrt(2-x))]dx as x goes from 0 to 1

    iv.) integral of Pi*[(x-1)-(sqrt(2-x-1)]dx as y goes from 0 to 1

    I think my definite integral limits are wrong... and in general my integral setup is wrong.. please help
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
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