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Using shell method to find the volume of a solid

  1. Sep 12, 2014 #1
    1. The problem statement, all variables and given/known data

    Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y=2x+15 and the parabola y=x2 about the following lines:

    a) The line x=5 b) The line x= -3 c) The x-axis d) The line y=25

    Note: leave answer in terms of pi

    2. Relevant equations

    v=2pi∫(shell radius)(shell height)

    3. The attempt at a solution

    I know that I am making a mistake somewhere; I have a feeling that it is in my set... I am hoping that someone will be able to point it out to me. I am stuck on part a) and if I figure out my mistake I am confident that I will be able to do the other parts of the problem.

    First thing that I did (after graphing which is attached) was find the limits of integration:
    2x+15=x2
    x2-2x-15
    (x-5)(x+3)
    So the limits of integration are from -3 to 5.

    v=2pi∫(5-x)(2x+15-x2)dx

    v=2pi∫10x+75-5x2-2x2-15x+x3

    v=2pi∫75-7x2-5x+x3

    v=2pi(75x-(7/3)x3-(5/2)x2+(1/4)x4

    (plug in the limits of integration)
    v=2pi [(2125/12)+(607/4)]

    v=2pi(1973/6)

    v=1973pi/3 <---this answer is wrong.

    I hope that someone will be able to help me with this, thanks for stopping by and sorry for the crappy paint graph.
     

    Attached Files:

  2. jcsd
  3. Sep 12, 2014 #2
    Your setup is fine, but your value for the primitive function at x=-3 is not correct. Try computing that particular value again. :)
     
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