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Math Help - Cylindrical shell question

  1. #1
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    Cylindrical shell question

    Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the y-axis.


    My graph is the parabola y=5x^2 up to the line x=1 and rotated around y axis and makes a bowl-like shape

    Formula for cylindrical shell:

    integral from a to b (2pi(r)(height)dy

    So I did integral from 0 to 1
    dy


    Am I correct or am I doing something wrong?


    Last edited by Steelers72; April 17th 2013 at 01:56 PM.
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    Re: Cylindrical shell question

    The region is you have specified is not bounded. Are you sure you copied it down right?
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    Re: Cylindrical shell question

    Sorry, I am not sure. I though the bounds are 0 and 1 since y=0 and x=1 but I guess that is incorrect.

    I solved y=5x^2 for x and got x= sqrt(y/5) but I am not sure where to go from there.

    formula for cylindrical is: integral a to b 2pi(radius)heightdy

    I am thinking the height is sqrt(y/5)? or do I have to subtract from the line x=1? Im a little perplexed with this problem.
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    Re: Cylindrical shell question

    Try drawing the region with your bounds, you'll see it is definitely not bounded. Perhaps you meant y = 1 instead of x = 1...
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    Re: Cylindrical shell question

    I figured this out:
    y=5x^2 , y=0 , x=1

    5x^2 being the height and x being the radius

    integral 0 to 1 2pi(x)*5x^2 dx

    10pi integral 0 to 1 x^3

    5pi/2 final ans.
    Last edited by Steelers72; April 20th 2013 at 01:10 PM.
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