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Math Help - volume of a solid rotated about the y-axis

  1. #1
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    volume of a solid rotated about the y-axis

    The problem is: If the region under the following curve from x = 0 to x = 1 is rotated about the y-axis, what is its volume?

    y= 6/(x^2+3x+2)


    In order to evaluate this, I use the cylindrical shell method by multiplying 2 pi by the function, right? please help!!
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  2. #2
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    Quote Originally Posted by DarthPipsqueak View Post
    The problem is: If the region under the following curve from x = 0 to x = 1 is rotated about the y-axis, what is its volume?

    y= 6/(x^2+3x+2)


    In order to evaluate this, I use the cylindrical shell method by multiplying 2 pi by the function, right? please help!!
    The curved surface area of a cylinder is 2{\pi}rh

    h is the value of the function for each value of x.
    x is the radius of the cylindrical shells.

    Integrating the cylindrical shell surface area from x=0 to x=1 will find the volume of revolution about the y axis.

    Hence, you must also multiply by x
    in order to get the curved surface area of all the shells.
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