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Math Help - solids of revolution

  1. #1
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    solids of revolution

    Find the volume of the resulting solid.
    (a) If the region under the following curve from x = 0 to x = 1 is rotated about the x-axis.


    (b) If the region under the following curve from x = 0 to x = 1 is rotated about the y-axis.


    I have NOOO idea what to do or how these volumes will be different..
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by khood View Post
    Find the volume of the resulting solid.
    (a) If the region under the following curve from x = 0 to x = 1 is rotated about the x-axis.


    (b) If the region under the following curve from x = 0 to x = 1 is rotated about the y-axis.


    I have NOOO idea what to do or how these volumes will be different..

    First, remember that regardless of how crazy the graph of this function is, you are only interested in the part of it between x=0 and x=1.

    If you are allowed, I would see what this looks like on a graphing calculator, just to get an idea of what you are working with. The part of this graph you are interested in is in quadrant I. In order to write your integrals, everything is given to you except you need to find where f(x) intercepts the y-axis, which you know you can find by solving for f(0). For this one, I would personally use the disk method for your rotation about the x axis and cylindrical shells about the y-axis.

    I assume you have learned the techniques you need to solve these and you just needed an idea of where to start? If you need more help, just ask!
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  3. #3
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    I got part b correct using shells like you suggested
    but I tried discs for part a and it ends up being a huge integral that i had to use partial fractions for and i could not get the right answer
    should it be as complicated as i made it or am i on the wrong path?
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