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Math Help - Help please!! - Volume using method of cylindrical shells

  1. #1
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    Help please!! - Volume using method of cylindrical shells

    Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y = 6sqrt(x) and y = 6x^2 about the y axis.
    I keep getting ~9.425 which is wrong, but I'm not sure why yet!
    Here is how I come to my answer time and time again...
    S = integral sign loL
    V = S 2pi(x(6sqrt(x) - 6x^2))
    V = 2pi S (6x - 6x^3)
    V = 2pi [3x^2 - (3/2)x^4] from 0-1
    V = 9.4248
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  2. #2
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    Hello, sgares!

    Your algebra is off . . .


    Use the method of cylindrical shells to find the volume of the solid obtained
    by rotating the region bounded by y \:= \:6\sqrt{x}\text{ and }y \:= \:6x^2 about the y-axis.
    Your set-up is correct . . .


    V \;=\;2\pi\int^1_0x\left(6x^{\frac{1}{2}} - 6x^2\right)\,dx


    But this is: . V \;=\;12\pi\int^1_0\left(x^{\frac{3}{2}} - x^3\right)\,dx

    . . . Try it now . . .

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  3. #3
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    Your set up seems correct. I think you just have an arithmetic error towards the end.

    2{\pi}\int_{0}^{1}\left[x(6\sqrt{x}-6x^{2})\right]dx=\frac{9{\pi}}{5}\approx{5.65}
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  4. #4
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    Haha wow! Embarrassing... thank goodness I didn't go to the engineering tutor center for this! This site seriously is the internets. Bookmarked for life.

    Thanks so much btw! )<
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