Calculus,Sketch a washer and Find the Volume of the Solid generatedBy Revolving the region bounded by y=2x^2, y=0, and x=2 around the y-axis?

1 Answer

  • Shell method:

    radius = x

    height = 2x^2

    Volume = 2 pi ∫ x (2x^2) dx , x=0 to 2

    = 4 pi ∫ x^3 dx , x=0 to 2

    = 16 pi

    Washer:

    Volume = pi ∫ (2^2 – (sqrt(y/2))^2 ) dy, y=0 to 8

    = pi ∫ (2^2 – y/2 ) dy, y=0 to 8

    = 16pi

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