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Math Help - Cylindrical Shell Method

  1. #1
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    Cylindrical Shell Method

    I need help asap. Finals in couple hours.

    f(x) = SquareRoot(x^2 + 9) over [0,3]

    I got 2pi integral from 0,3 and inside of integral i put x(SquareRoot(x^2 + 9)dx.

    I know that I'm suppose to multiply it out but I dont know how to im suppose to multiply that because of the square root. help would be appreciated.

    Sorry for not using the symbolic characters.
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  2. #2
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    You didn't say which axis you have to revolve it around. y axis?.
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  3. #3
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    yes, sorry. the y-axis.
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  4. #4
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    In that event, you set up is correct.

    2{\pi}\int_{0}^{3}x\sqrt{x^{2}+9}dx

    Now, let u=x^{2}+9, \;\ du=2xdx, \;\ \frac{1}{2}du=xdx

    Don't forget to change your limits of integration:

    (3)^{2}+9=18, \;\ (0)^{2}+9=9

    So, your new limits are 9 to 18 and you have:

    {\pi}\int\sqrt{u}du
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