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Math Help - Cylindrical shell (Check my answer)

  1. #1
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    Exclamation Cylindrical shell (Check my answer)

    Question :

    Find the volume of the solid generated if the region bounded by the curve y=x^2 , x=1 is revolved about x=0.

    Attempt:

    I drew the figure and got ;

    V=2\pi r h t

     2\pi [\frac{x^3}{3}-\frac{x^4}{4}]\int -limit from 1 to 0

    = \frac{\pi}{6}
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  2. #2
    Junior Member eddie2042's Avatar
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    Quote Originally Posted by mj.alawami View Post
    Question :

    Find the volume of the solid generated if the region bounded by the curve y=x^2 , x=1 is revolved about x=0.

    Attempt:

    I drew the figure and got ;

    V=2\pi r h t

     2\pi [\frac{x^3}{3}-\frac{x^4}{4}]\int -limit from 1 to 0

    = \frac{\pi}{6}
    You were mostly right. It should be

    V = \int_0^1 2\pi rh
    V = 2\pi \int_0^1 x [x^2] dx
    V = 2\pi \left[\frac{x^4}{4}\right]_0^1
    V = \frac{\pi}{2}
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